geodynamics of earth’s deep mantle

178
Geodynamics of Earth’s Deep Mantle Thesis by Dan J. Bower In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2012 (Defended May 1 st , 2012)

Upload: others

Post on 09-Feb-2022

5 views

Category:

Documents


0 download

TRANSCRIPT

Geodynamics of Earth’s Deep Mantle

Thesis by

Dan J. Bower

In Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

California Institute of Technology

Pasadena, California

2012

(Defended May 1st, 2012)

ii

c© 2012

Dan J. Bower

All Rights Reserved

iii

Geology is the study of pressure and time. That’s all it takes really, pressure, and

time. That, and a big goddamn poster.

—Ellis Boyd ‘Red’ Redding, The Shawshank Redemption

iv

Acknowledgements

Embarking on an intrepid voyage of discovery to the deep Earth would not have been

possible without the inspiring guidance of my Navigation Officer, Mike Gurnis. I

thank you for posing thought-provoking, challenging, and diverse research questions

and ensuring safe passage through uncharted waters. Whenever I felt lost at sea our

discussions would invariably steer me back on course. Furthermore, I appreciate the

supportive, collaborative, and vibrant research environment that you foster and your

timely, focused feedback on manuscripts.

I am most grateful to Jennifer Jackson for ensuring that I did not run aground in

the shallow waters of mineral physics. And Don Helmberger for instilling confidence

that I would not capsize in the unpredictable waves of seismology. Additionally,

thanks for your frequent reminders that “the Earth is real complicated”. The freedom

to venture into these disciplines greatly broadened my depth of knowledge and ability

to tackle multifaceted research problems.

My watchmen, Paul Asimow and Dave Stevenson, ensured plain sailing by main-

taining a clear view of the horizon to spot uncertain weather and hazards from afar.

I appreciate your measured advice, and several of your insights and suggestions fea-

ture in this Captain’s Log. Field trip leaders including Jason Saleeby, John Eiler,

v

Jean-Philippe Avouac, Rob Clayton, and Joann Stock, enticed me to flirt with the

“shallow subsurface” (less than 670 km depth), although my heart always remained

true to structure below the transition zone.

Senior explorers, Drs. Eh Tan and Daoyuan Sun, graciously provided mentorship

and expertise when I was a fledgling adventurer learning the ropes. A gifted and

extensive crew also offered encouragement throughout the mission: in particular,

discussions with Dr. Lijun Liu, June Wicks, Aaron Wolf, and Laura Alisic uncovered

common ground between my own research and other fields. My office mates and I

engaged in stimulating discussions and good-spirited humor: Dr. Eun-Seo Choi, Dr.

Ravi Kanda, Dr. Michelle Selvans, Zhongwen Zhan, Dongzhou Zhang, Yingdi Luo,

and Chris Rollins.

The warm and positive atmosphere within the Seismological Laboratory and GPS

division solidifies their reputation as truly extraordinary venues for conducting re-

search. This environment is amplified by the thoughtful and caring staff, including

Viola Carter and Dian Buchness. I thank the Computational Infrastructure for Geo-

dynamics (CIG), GPlates developers, and collaborators at the University of Sydney,

for supplying source code and datasets. I am grateful to Naveed Near-Ansari, John

Lilley, Mike Black, and Scott Dungan for their exceptional administration of comput-

ing resources and rapid response to e-mail queries. Mark Turner introduced me to

the power of Python and programming paradigms.

Involvement with numerous campus organizations and activities ensured that I

remained on an even keel during my journey to the deep Earth. These include athletic

vi

endeavours, dance, social and environmental activism, and student council. Through

these activities I have built a global friendship circle of talented individuals who

passionately champion a cause alongside their academic obligations. It is impossible

to acknowledge the many friendships that enrich my life; for brevity I include the

Chapmans, Matzens, Kelbers (soon to be), Dolbys (also soon to be), Steve Chemtob,

and Kristin Phillips. I thank Pratyush Tiwary and Patrick Sanan for spearheading

regular exoduses to mountainous terrain and the camaraderie within the Caltech

Alpine Club.

Frequent radio contact with friends and family at my home port helped me to ride

out stormy weather during my adventure. I am indebited to my parents and sister

for always believing I could walk on water and enabling me to venture to the new

world. I remain buoyed up by your love and support. Final thanks to my stowaway,

Danielle Bower, for providing endless distractions en route, and for sailing into the

sunset with me.

vii

Abstract

Seismic tomography and waveform modeling reveal several prominent structures in

the Earth’s lower mantle: (1) the D′′ discontinuity, defined by a seismic velocity in-

crease of 1–3% about 250 km above the core-mantle boundary (CMB), (2) Ultralow-

velocity zones (ULVZs), which are thin, isolated patches with anomalously low seis-

mic wavespeed at the CMB, and (3) two large, low-shear velocity provinces (LLSVPs)

beneath Africa and the Pacific Ocean. The geodynamics of these structures are in-

vestigated using numerical convection models that include new discoveries in mineral

physics and recent insight from seismology. In addition, I assess the influence of an

iron spin transition in a major lower mantle mineral (ferropericlase) on the style and

vigor of mantle convection.

A phase change model for the D′′ discontinuity produces significant thermal and

phase heterogeneity over small distances due to the interaction of slabs, plumes, and

a phase transition. Perturbations to seismic arrivals are linked to the evolutionary

stage of slabs and plumes and can be used to determine phase boundary properties,

volumetric wavespeed anomaly beneath the discontinuity, and possibly the lengthscale

of slab folding near the CMB.

I simulate convection within D′′ to deduce the stability and morphology of a

viii

chemically distinct iron-enriched ULVZ. The chemical density anomaly largely dic-

tates ULVZ shape, and the prescribed initial thickness (proxy for volume) of the

chemically distinct layer controls its size. I synthesize the dynamic results with a

Voigt-Reuss-Hill mixing model to provide insight into the inherent seismic trade-off

between ULVZ thickness and wavespeed reduction.

The dynamics of the LLSVPs are investigated using global 3-D models of ther-

mochemical structures that incorporate paleogeographic constraints from 250 Ma to

present day. The structures deform and migrate along the CMB, either by coupling

to plate motions or in response to slab stresses. Slabs from Paleo-Tethys and Tethys

Ocean subduction push the African structure further to the southwest than inferred

from tomography. Dense and viscous slabs can severely compromise the stability of

thermochemical structures with a high bulk modulus at the CMB.

Finally, I explore the consequences of the intrinsic density change caused by the

Fe2+ spin transition in ferropericlase on the style and vigor of mantle convection. The

transition generates a net driving density difference for both upwellings and down-

wellings that dominantly enhances the positive thermal buoyancy of plumes in 2-D

cylindrical geometry. Although the additional buoyancy does not fundamentally alter

large-scale dynamics, the Nusselt number increases by 5–10%, and vertical velocities

increase by 10–40% in the lower mantle. Advective heat transport is more effective

and temperatures in the CMB region are reduced by up to 12%.

ix

Contents

Acknowledgements iv

Abstract vii

List of Figures xii

List of Tables xiv

1 Introduction 1

2 Dynamic origins of seismic wavespeed variation in D′′ 8

2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Numerical convection models . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2 Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.3 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.4 Post-perovskite phase transition . . . . . . . . . . . . . . . . . 17

2.4 Seismic waveform modeling . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

x

2.5.1 Overview of D′′ slab dynamics . . . . . . . . . . . . . . . . . . 22

2.5.2 Overview of seismic wavespeed anomalies . . . . . . . . . . . . 24

2.5.3 Dynamic and seismic variations . . . . . . . . . . . . . . . . . 28

2.5.4 Waveform predictions . . . . . . . . . . . . . . . . . . . . . . . 32

2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3 A model of a solid-state ultralow-velocity zone 44

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.3.1 Equations and solution methods . . . . . . . . . . . . . . . . . 48

3.3.2 Domain and rheology . . . . . . . . . . . . . . . . . . . . . . . 51

3.3.3 Boundary and initial conditions . . . . . . . . . . . . . . . . . 52

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.1 Transient period . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.2 Steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Geodynamic consequences of the spin transition in ferropericlase 76

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.3 Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

xi

4.3.1 Spin buoyancy formulation . . . . . . . . . . . . . . . . . . . . 78

4.3.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . 85

5 Paleogeographically constrained dynamic Earth models 87

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3 Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.3.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . 95

5.3.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.3.3 Data assimilation . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3.4 Parameter space . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3.5 Initial condition . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A Derivation of the mineral physics derivatives 127

Bibliography 130

xii

List of Figures

2.1 Geotherms and reference adiabat for D′′ models . . . . . . . . . . . . . 21

2.2 Evolution of a slab in D′′ . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 P- and S-wave velocity of a slab in D′′ . . . . . . . . . . . . . . . . . . 26

2.4 D′′ dynamic outcomes from parameter variation . . . . . . . . . . . . . 29

2.5 S-wave velocity from parameter variation . . . . . . . . . . . . . . . . . 30

2.6 Synthetic seismograms for a slab in D′′ . . . . . . . . . . . . . . . . . . 33

2.7 Synthetic seismograms from parameter variation I . . . . . . . . . . . . 34

2.8 Synthetic seismograms from parameter variation II . . . . . . . . . . . 35

3.1 Representative behavior of a model during the transient period . . . . 55

3.2 Relief of the structures at steady state (all models) . . . . . . . . . . . 58

3.3 Relief of the structures at steady state (subset of models) . . . . . . . 59

3.4 Half-width of the structures at steady state . . . . . . . . . . . . . . . 60

3.5 Aspect ratio (relief/half-width) of the structures at steady state . . . . 61

3.6 Steady-state behavior of a thin (Mg,Fe)O-containing layer . . . . . . . 64

3.7 Voigt-Reuss-Hill wavespeed determinations and relief of structures . . . 68

3.8 Comparison of P-wave seismic data and solid-state model prediction . 71

3.9 Comparison of S-wave seismic data and solid-state model prediction . . 72

xiii

4.1 Snapshot from case 13 at quasi-steady state . . . . . . . . . . . . . . . 81

4.2 Fractional change in vertical velocity and temperature . . . . . . . . . 82

5.1 Seismic tomography data for the LLSVPs . . . . . . . . . . . . . . . . 90

5.2 Snapshots of the plate tectonic reconstruction . . . . . . . . . . . . . . 101

5.3 Progressive data assimilation example (model EX1) . . . . . . . . . . . 103

5.4 Thermochemical extended-Boussinesq reference model (EX1) . . . . . 107

5.5 Thermochemical domes and thermal plumes (EX1) . . . . . . . . . . . 109

5.6 Unstable domes at the core-mantle boundary (BO1) . . . . . . . . . . 111

5.7 Model comparison of assimilation (BO2) and kinematic only (BO3) . . 112

5.8 Thermochemical Boussinesq reference model (BO5) . . . . . . . . . . . 113

5.9 Motion and deformation of the domes . . . . . . . . . . . . . . . . . . 117

5.10 3-D view of the domes (BO5) . . . . . . . . . . . . . . . . . . . . . . . 120

5.11 Radial profiles for viscosity, sinking speed, and age-depth relation . . . 123

xiv

List of Tables

2.1 Generic model parameters for D′′ slabs . . . . . . . . . . . . . . . . . . 19

2.2 Model specific parameters for D′′ slabs . . . . . . . . . . . . . . . . . . 19

3.1 ULVZ model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.1 Input and output characteristics of the models with spin buoyancy. . . 83

5.1 Generic geodynamic parameters for thermochemical structures . . . . . 97

5.2 Model-specific parameters for thermochemical structures . . . . . . . . 105

1

Chapter 1

Introduction

Unveiling the nature of the deep Earth demands a multidisciplinary approach and

there are exciting new research directions at the intersection of mineral physics, seis-

mology, and geodynamics. Seismic methods provide the most comprehensive sampling

of the mantle and constrain wavespeeds, the sharpness of features, and the geograph-

ical distribution of heterogeneity. The dominant lower mantle minerals are aluminous

ferromagnesian silicate perovskite, (Mg,Fe,Al)(Si,Al)O3, and magnesium iron oxide,

(Mg,Fe)O, which occupy about 75 and 15 volume percent of the lower mantle, respec-

tively (Ringwood , 1991). Recent advancements in mineral physics, notably diamond

anvil cell technology, are enabling experimentalists to determine the wavespeeds and

material properties of these phases to compare with seismic and dynamic inferences.

New discoveries in the behavior of (Mg,Fe)SiO3 and (Mg,Fe)O at extreme conditions

motivate the research presented in three chapters of this thesis. Convection calcula-

tions elucidate how mass and heat transfer influence the morphology, stability, and

longevity of structures in the mantle.

The core-mantle boundary (CMB) (3300–4400 K) separates the liquid iron-rich

outer core from the solid silicate mantle at ∼ 2890 km depth (e.g., Lay et al., 2008).

2

This interface defines the largest contrast in material and dynamic properties in the

Earth. The high viscosity subsolidus lower mantle deforms by slow, creeping flow (∼

1 cm/yr) (e.g., Davies , 1999), whereas the inviscid outer core is rapidly convecting

(∼ 1 mm/s) (e.g., Glatzmaier and Roberts , 1995). Heat transfer across the CMB

occurs predominantly by conduction and mass exchange is negligible. Total heat flow

from the core to the mantle controls the power available to drive the geodynamo,

the cooling rate of the core, and the growth rate of the inner core. The outer core

boundary behaves as an isothermal free-slip surface to mantle convection because of

the vastly different timescales associated with core and mantle dynamics.

Seismic waveform modeling elucidates the fine-scale features of the CMB region

through the analyses of wavetrains that arrive before or after well-identified reference

phases on seismograms. These wavetrains are sometimes visible on individual seis-

mograms or may require data stacking to increase the signal-to-noise ratio. Arrivals

with neighboring raypaths can be analyzed together to eliminate source dependency

and constrain mantle heterogeneity along a particular segment of a propagation path.

Waveform modeling can often distinguish between volumetric heterogeneity and sharp

seismic gradients and has proven instrumental in shaping our view of the CMB region.

Lay and Helmberger (1983) discovered the D′′ discontinuity, a seismic interface

characterized by a shear velocity increase of 1–3% approximately 250 km above the

CMB. The boundary is inferred from an extra phase, known as SdS, that arrives

between the direct S-wave, S, and the core-reflected S-wave, ScS, at post-critical dis-

tances. SdS turns in the higher velocity layer below the discontinuity, which produces

3

a triplication in seismic data. Seismologists identify the triplication beneath regions

of inferred paleosubduction including Alaska, the Caribbean, Central America, India,

and Siberia. Detections beneath the seismically slow central Pacific are contrary to

this trend and may suggest that the discontinuity height above the CMB or velocity

increase are modulated by composition.

There are three probable explanations for the discontinuity, which are not neces-

sarily mutually exclusive: phase change, thermal heterogeneity, or a chemical bound-

ary. A phase change best explains the seismic data (Sidorin et al., 1998). Contary

to observations, thermal heterogeneity alone does not produce a strong SdS arrival,

and a pre-existing chemical layer is pushed away from downwelling regions. Subse-

quent experimental and theoretical verification of a phase transition in MgSiO3 from

silicate perovskite, the major phase of the lower mantle, to a new phase, termed

“post-perovskite”, supports the phase change interpretation (Murakami et al., 2004;

Oganov and Ono, 2004). Furthermore, a “double crossing” of the phase boundary

may explain neighboring seismic discontinuities (Hernlund et al., 2005).

In Chapter 2 I investigate the fine-scale interaction of a slab as it descends through

the phase transition and perturbs the thermal boundary layer at the CMB. The

temperature anomalies of slabs and plumes elevate and suppress the phase boundary,

respectively. I elucidate the expected perturbations to temperature and phase that

map to variations in seismic structure and produce waveform complexity in synthetic

seismograms. Modern three-component broadband seismic arrays such as USArray

will provide data to compare with the predictions.

4

Ultralow-velocity zones (ULVZs) are thin (< 100 km), isolated patches with

anomalously low seismic wavespeed (reductions of ∼ 10–30%) at the CMB originally

detected beneath the western Pacific but since discovered in other regions. They

were identified by the late arrival of the seismic phase SPdKS relative to SKS for dis-

tances between 105 and 120 degrees. SKS travels through the mantle and outer core

and SPdKS follows a similar path except for a short diffracted segment (Pd) along

the CMB. Waveform modeling using differential travel time and amplitude therefore

constrains the P-wave velocity for this segment. Additionally, precursors and postcur-

sors to core-reflected phases (PcP, ScP, ScS) can potentially constrain the P and S

wavespeed, thickness, and density of ULVZs, although data stacking is required to

enhance the signal-to-noise ratio.

Iron enrichment of solid phases, specifically the increase in Fe/(Fe+Mg) ratio, can

simultaneously increase density and reduce compressional and shear velocity (e.g.,

Karato and Karki , 2001). This partly inspired the notion of solid, iron-rich ULVZs,

such as a metal-bearing layer (Knittle and Jeanloz , 1991; Manga and Jeanloz , 1996),

subducted banded iron formations (Dobson and Brodholt , 2005), or iron-enriched

post-perovskite (Mao et al., 2006; Stackhouse and Brodholt , 2008). Iron-rich systems

are typically denser than the surrounding mantle, which is required to explain the

locations of ULVZs at the base of the mantle.

Recent high-pressure experiments have uncovered very low sound velocities in iron-

rich (Mg,Fe)O that could explain the origin of some ULVZs (Wicks et al., 2010). I ex-

plore this hypothesis in Chapter 3 by developing a thermochemical convection model

5

of a solid-state ULVZ that contains a small volume fraction of iron-rich (Mg,Fe)O. A

mineral physics mixing model combines the material properties for the oxide phase

and ambient material using select chemical partitioning models to determine the ther-

moelastic parameters of the assemblage. The model satisfies current seismic modeling

constraints.

The behavior of (Mg,Fe)O at high pressure and temperature conditions also mo-

tivates the study presented in Chapter 4. A high-spin (four unpaired d electrons) to

low-spin (no unpaired d electrons) electronic transition of ferrous iron in an octahe-

dral local environment increases the density of (Mg,Fe)O ferropericlase by 2–4% at

mid-lower mantle pressure around 50 GPa (Sturhahn et al., 2005; Badro et al., 2003).

This transformation occurs over a pressure range that is small at ambient tempera-

ture (∼ 300 K) and broad at high temperature (∼ 3000 K). The spin transition is

continuous along a lower mantle geotherm (Sturhahn et al., 2005; Tsuchiya et al.,

2006). However, downwellings and upwellings may generate substantial temperature

anomalies in the mantle, so that convective flow may be modified by buoyancy forces

arising through the spin-state of the material.

I investigate how the spin transition in (Mg,Fe)O impacts the large-scale style and

vigor of mantle convection in Chapter 4. The body-force due to the spin-state of the

material is included in the momentum equation. To determine the influence of the

spin transition I observe the pattern of convection, time average heat flux, and time

average depth profiles for the horizontally averaged temperature and RMS vertical

velocity.

6

Seismic tomography reveals two antipodal large, low-shear velocity provinces

(LLSVPs) at the base of the mantle beneath the Pacific Ocean and Africa. The

circum-Pacific belt of fast material is attributed to relic slabs from paleosubduction

(Richards and Engebretson, 1992). The LLSVPs occupy approximately 20% of the

surface area of the CMB and contain about 1.6 vol. % and 1.9 mass % of the mantle

(e.g., Burke et al., 2008). Ni and Helmberger (2003a) model the 3-D geometry of

the African LLSVP as a ridge-like structure approximately 1200 km high and 1000

km wide that extends 7000 km from central Africa to the Indian Ocean. The Pacific

LLSVP may be divided into a western province that is 1000 km wide and rises 740

km above the CMB and an eastern section that is 1800 km wide and 340–650 km

high (He and Wen, 2009).

A thermochemical origin is necessary to explain anti-correlated shear wave and

bulk sound velocity anomalies (Su and Dziewonski , 1997; Masters et al., 2000), puta-

tive anti-correlated shear wave and density anomalies (Ishii and Tromp, 1999, 2004),

multipathing for waves sampling its steep edges (Ni et al., 2002), and geological infer-

ences of stability over 200–300 Myr (Burke and Torsvik , 2004). These observations

are suggestive of a material with a higher bulk modulus and higher zero-pressure den-

sity than ambient mantle (Tan and Gurnis , 2005). Furthermore, surface plate history

influences the morphology and location of the LLSVPs (McNamara and Zhong , 2005).

In Chapter 5 I investigate the response of high bulk modulus structures in the

lower mantle to evolving surface tectonics from 250 Ma to present day. A novel

time-dependent thermal and kinematic boundary condition is derived from a high-

7

resolution plate history model that encodes global plate motions and paleosubduction

locations. These paleogeographic constraints are incorporated into 3-D spherical con-

vection models with a high bulk modulus material with a higher zero-pressure density

than ambient mantle.

8

Chapter 2

Dynamic origins of seismic

wavespeed variation in D′′

To be submitted as:

Bower, D. J., M. Gurnis, and D. Sun (2012), Dynamic origins of seismicwavespeed variation in D′′, Phys. Earth Planet. In.

2.1 Abstract

The D′′ discontinuity is defined by a seismic velocity increase of 1–3% about 250 km

above the core-mantle boundary (CMB), and is mainly detected beneath locations

of inferred paleosubduction. A phase change origin for the interface can explain a

triplicated arrival observed in seismic waveform data and is supported by the re-

cent discovery of a post-perovskite phase transition. We investigate the interaction

of slabs, plumes, and the phase change within D′′ in 2-D compressible convection

calculations, and predict waveform complexity in synthetic seismic data. The dy-

namic models produce significant thermal and phase heterogeneity in D′′ over small

distances and reveal a variety of behaviors including: (1) distinct pPv blocks sepa-

rated by upwellings, (2) notches at the top of a pPv layer caused by plume heads, (3)

9

regions of Pv embedded within a pPv layer due to upwellings. Advected isotherms

produce complicated thermal structure that enable multiple crossings of the phase

boundary. Perturbations to S, SdS, and ScS arrivals (distances < 84 degrees) are

linked to the evolutionary stage of slabs and plumes, and can be used to determine

phase boundary height and velocity increase, volumetric wavespeed anomaly beneath

the discontinuity, and possibly the lengthscale of slab folding near the CMB. Resolv-

ing fine-scale structure beneath the interface requires additional seismic phases (e.g.,

Sd, SKS) and larger distances (> 80 degrees).

2.2 Introduction

The D′′ discontinuity is characterized by a seismic velocity increase of 1–3% ap-

proximately 250 kilometers above the core-mantle boundary (CMB) (see review by

Wysession et al., 1998). Seismic waveform modeling detects a velocity jump beneath

locations of inferred paleosubduction, including Alaska, the Caribbean, Central Amer-

ica, India, and Siberia. Furthermore, in seismic tomography the high velocity and

deep anomalies in these regions are interpreted as slabs (e.g., Grand , 2002).

The discontinuity can explain a triplicated arrival SdS (PdP) between S (P) and

ScS (PcP) observed in waveform data (Lay and Helmberger , 1983). Between epicen-

tral distances 65–83 degrees, SdS is a composite arrival from a discontinuity reflection

Sbc (Pbc) and a ray turning below the interface Scd (Pcd). The horizontally-polarized

S-wave (SH) triplicated arrival is often analyzed at ∼ 10 s period and is not contam-

inated by other phases or mode conversions. Shorter periods (∼ 1 s) can detect the

10

P-wave triplication (PdP) but data stacking is required to suppress noise.

There are generally fewer or weaker SdS (PdP) detections outside high-velocity

areas which suggests subduction history influences the presence and strength of the

arrival. In contrast to seismic observations, a pre-existing basal chemical layer gener-

ates strong (weak) SdS below upwellings (downwellings) (Sidorin and Gurnis, 1998;

Sidorin et al., 1998) and does not generate short wavelength heterogeneity on the dis-

continuity (Tackley , 1998). However, detections of SdS beneath the seismically slow

central Pacific suggest the discontinuity height above the CMB or velocity increase

may be modulated by composition in some regions (Garnero et al., 1993a).

Early dynamic calculations and waveform modeling propose a thermal slab inter-

acting with a phase change with a positive Clapeyron slope can explain the origin

of the D′′ discontinuity (Sidorin et al., 1999a, 1998). Incident rays are refracted by

a high velocity thermal slab above D′′ and turn beneath the discontinuity in the

higher velocity phase to produce the SdS arrival. Furthermore, a high-temperature

thermal boundary layer generates a negative seismic velocity gradient at the CMB.

This counteracts the velocity step to ensure that differential travel times (e.g., ScS–S)

and diffracted waveforms match data (Young and Lay , 1987, 1990). Sidorin et al.

(1999b) unify regional seismic models from waveform studies by proposing a global

discontinuity with an ambient phase change elevation of 200 km above the CMB and

a Clapeyron slope of 6 MPa K−1. The actual boundary locally is thermally perturbed

upward and downward.

The subsequent discovery of a phase transition in MgSiO3 from silicate perovskite

11

(Pv) to “post-perovskite” (pPv) at CMB conditions supports the phase change hy-

pothesis (Murakami et al., 2004; Oganov and Ono, 2004). Ab initio calculations at 0

K suggest that the transformation of isotropic aggregates of Pv to pPv increases the

S-wave velocity by 1–1.5% and changes the P-wave velocity by -0.1–0.3% (Oganov

and Ono, 2004; Tsuchiya et al., 2004; Iitaka et al., 2004). First principle calculations

at high temperature produce similar wavespeed variations (Stackhouse et al., 2005;

Wentzcovitch et al., 2006), and high pressure experiments resolve a 0–0.5% increase

in S-wave velocity (Murakami et al., 2007). Lattice-preferred orientation in the pPv

phase may reconcile the small variation in wavespeeds from mineral physics with the

1–3% increase across the D′′ discontinuity deduced from seismic data (e.g., Wookey

et al., 2005). Fe content in Pv may decrease (Mao et al., 2004) or increase (Tateno

et al., 2007) the phase transition pressure, and Al may broaden the mixed phase

region (Catalli et al., 2010; Akber-Knutson et al., 2005). However, other researchers

find that compositional variations have little effect (Hirose et al., 2006; Murakami

et al., 2005). Independent of the width of the mixed phase region, strain-partitioning

into weak pPv can produce a sharp seismic discontinuity due to the rapid change in

seismic anisotropy (Ammann et al., 2010).

The phase transformation destabilizes the lower thermal boundary layer, which

produces more frequent upwellings (Sidorin et al., 1999a; Nakagawa and Tackley ,

2004). A dense basal layer interacting with a chemically heterogeneous slab and the

Pv-pPv transition produces strong lateral gradients in composition and temperature

that may also explain finer structure within D′′ (Tackley , 2011). A “double crossing”

12

of the phase boundary occurs when pPv transforms back to Pv just above the CMB

and may explain neighboring seismic discontinuities (Hernlund et al., 2005). However,

the precritical reflection from the second putative phase transition is a relatively low

amplitude arrival and therefore difficult to detect (Flores and Lay , 2005; Sun et al.,

2006). The Clapeyron slope and transition temperature (or pressure) control the

topography of the pPv layer (e.g., Monnereau and Yuen, 2007),

The CMB beneath Central America is illuminated through the propagation of

seismic waves along a narrow corridor from South American subduction zone events

to broad-band networks in North America. Furthermore, seismic tomography and

plate reconstructions indicate deeply penetrating slab material (e.g., Grand , 2002;

Ren et al., 2007). Under the Cocos Plate, the D′′ discontinuity can be modeled at

constant height above the CMB with S-wave variations of 0.9–3.0% (Lay et al., 2004;

Ding and Helmberger , 1997) or as an undulating north–south dipping structure from

300 km to 150 km above the CMB with constant D′′ velocity (Thomas et al., 2004).

The Pv-pPv transition may account for the positive jump seen in S-wave models and

smaller negative P-wave contrast (Hutko et al., 2008; Kito et al., 2007; Wookey et al.,

2005). Furthermore, its interaction with a buckled slab may explain an abrupt 100

km step in the discontinuity (Sun and Helmberger , 2008; Hutko et al., 2006; Sun et al.,

2006). A second deeper negative reflector appears in some locations about 200 km

below the main discontinuity. This may originate from the base of a slab, a plume

forming beneath a slab (Tan et al., 2002), back-transformation of pPv-Pv, chemical

layering (Kito et al., 2007; Thomas et al., 2004), or out-of-plane scatterers (Hutko

13

et al., 2006).

It is now timely to reanalyze the role of slabs in the deep mantle and their seismic

signature following discovery of the Pv-pPv transformation and a proposed “double

crossing” of the phase boundary. In this study we follow a similar approach to Sidorin

et al. (1998) using a compressible formulation and viscoplastic rheology. Compress-

ibility promotes an irregular, more sluggish, flow field and encourages greater interac-

tion between upper and lower boundary instabilities (Steinbach et al., 1989). Viscous

heating redistributes buoyancy sources (Jarvis and McKenzie, 1980) and latent heat

can reverse phase boundary distortion caused by the advection of ambient temper-

ature (Schubert et al., 1975). These non-Boussinesq effects could play an important

role in determining the lateral variations in temperature and phase that may give

rise to rapidly varying waveforms. Using constraints from experimental and theoret-

ical mineral physics we predict seismic wavespeed structure from the temperatures

and phases determined by the convection calculations. Finally, we compute synthetic

seismograms to analyze S, SdS, and ScS arrivals.

2.3 Numerical convection models

2.3.1 Equations

We employ the truncated anelastic liquid approximation (TALA) for infinite-Prandtl-

number flow (Jarvis and McKenzie, 1980; Ita and King , 1994) with a divariant phase

change using CitcomS (Zhong et al., 2000; Tan et al., 2007). The conservation equa-

14

tions of mass, momentum, and energy (non-dimensional) are:

(ρui),i = 0 (2.1)

−P,i + τij,j = (RbΓ − RaραT )gδir (2.2)

τij = η

(

ui,j + uj,i −2

3uk,kδij

)

(2.3)

ρc′(T,t + uiT,i) = ρcκT,ii − ρgα′urDi(T + TS) +Di

Raτijui,j + ρH (2.4)

where ρ is density, u velocity, P dynamic pressure, τ deviatoric stress tensor, Ra

thermal Rayleigh number, α thermal expansivity, T temperature, Rb phase Rayleigh

number, Γ phase function, g gravitational accceleration, η viscosity, t time, c heat

capacity, κ thermal diffusivity, TS surface temperature, Di = α0g0R0/cp0 dissipation

number, and H internal heat production rate. Depth-dependent reference state pa-

rameters are denoted by overbars, and the r subscript denotes a unit vector in the

radial direction. Phase buoyancy and latent heat are included using a phase func-

tion Γ, effective heat capacity c′, and effective thermal expansivity α′ (Richter , 1973;

Christensen and Yuen, 1985), defined as:

Γ(ph, TΓ) =1

2

(

1 + tanh

(

ph − pΓ − γ(T − TΓ)

d

))

(2.5)

α′/α = 1 + γRb

Ra

∂Γ

∂ph

(2.6)

c′/c = 1 + Di(T + TS)γ2 Rb

Ra

∂Γ

∂ph

(2.7)

15

where (pΓ, TΓ) is the reference pressure and temperature of the phase transition, γ

Clapeyron slope, d phase transition width, and ph hydrostatic pressure. The phase

function Γ = 0 for Pv and Γ = 1 for pPv.

The thermal Rayleigh number, Ra is defined by dimensional surface values:

Ra =ρ0α0∆TR0

3g0

η0κ0

. (2.8)

Our Ra is therefore about an order-of-magnitude larger than a definition with mantle

thickness (Table 2.1).

2.3.2 Rheology

We use a temperature-dependent viscosity, governed by an Arrhenius law, and with

plastic yielding to generate a mobile upper surface and strong slabs (Moresi and

Solomatov , 1998; Tackley , 2000):

η(T ) = exp( 20

T + 1−

20

2

)

. (2.9)

The reference viscosity η0 is defined at the CMB (T = 1). We define the strength

envelope of the lithosphere using Byerlee’s Law (Byerlee, 1978):

σ(r) = min[a + b(1 − r), σy] (2.10)

16

where r is the radius, σ yield stress, a cohesion, b brittle stress gradient, and σy

ductile yield stress. The effective viscosity ηeff is computed by:

ηeff = min[

η(T ),σr(r)

]

(2.11)

where ǫ is the second invariant of the strain rate tensor.

The cohesion is set to a small value a = 1 × 104, and remains constant to limit

the number of degrees of freedom. We define a yield stress envelope characterized by

brittle failure from the surface to 160 km depth and ductile failure for greater depths

(b = 40σy). Preliminary models reveal b = 1.6×109 produces plate-like behavior with

strong downwellings.

2.3.3 Model setup

We solve the conservation equations in a 2-D cylindrical section (2 radians) with free-

slip and isothermal upper and lower surfaces and zero heat flux sidewalls. Internal

heating is neglected (H = 0). Radial mesh refinement provides the highest resolution

of 14 km within the thermal boundary layers and the lowest resolution of 40 km in the

mid-mantle. Lateral resolution is 0.45 degrees (50 and 28 km at the top and bottom,

respectively).

We construct a depth-dependent reference state for density using a polynomial fit

to PREM in the lower mantle (Solheim and Peltier , 1990; Dziewonski and Anderson,

1981). The pressure-dependence of the thermal expansion coefficient is derived from

experimental data for MgSiO3 (Mosenfelder et al., 2009) and varies by approximately

17

a factor of 4 across the mantle. Gravity and heat capacity are approximately constant

throughout the mantle and therefore we adopt uniform profiles. Thermal conductiv-

ity is likely dependent on pressure and temperature, although there are significant

uncertainties, particularly in multi-phase and chemically complex systems. We choose

to neglect this complexity by assigning the same thermal conductivity to Pv and pPv

independent of pressure.

The initial condition is derived from a precalculation (extended-Boussinesq) with

similar parameters (Table 2.1) while excluding the phase transition. This reduces the

spin-up time for the TALA model. We integrate the model for several 10,000s of time

steps (dimensionally several Gyr) such that the initial condition no longer affects our

results.

2.3.4 Post-perovskite phase transition

We set the ambient phase transition temperature (TΓ = 2600 K) to the horizontally

averaged temperature 300 km above the CMB in the precalculation. The free param-

eters are the ambient phase transition pressure pΓ and the Clapeyron slope γ, which

we vary to explore a range of dynamic scenarios and consequences for seismic wave

propagation. The Clapeyron slope is varied between 7.5 MPa K−1 and 13.3 MPa

K−1, which is consistent with geophysical constraints (Hernlund and Labrosse, 2007)

and mineral physics theory and experiment (see review by Shim, 2008). Sidorin et al.

(1999b,a) favor a Clapeyron slope of 6 MPa K−1, although larger values fit the data

nearly as well.

18

The interaction of a simple conductive geotherm with the phase transition can

produce a double crossing of the phase boundary (Hernlund et al., 2005). Ambient

mantle enters the pPv stability field in D′′ and then transforms back to Pv just

above the CMB. In this scenerio a double crossing occurs when the phase transition

temperature at the CMB is less than the CMB temperature. This is in part because

a conductive temperature profile increases monotonically with pressure. However,

temperature profiles that sample thermal heterogeneity in D′′ (slabs, plumes) can

intersect the pPv phase space multiple times even for phase transition temperatures

that are greater than the CMB temperature. The CMB is an isothermal boundary

so we can always compute the stable phase at the base of the mantle for each model

a priori (Table 2.2). If pPv is stable at the CMB, at least one phase transition must

occur independent of temperature. If Pv is stable, a double crossing is facilitated for

mantle regions in the pPv stability field.

2.4 Seismic waveform modeling

We express the relative perturbation to a parameter X using the notation δX =

∂lnX ≡ ∆X/X where ∆X is the change in X. The perturbation to the P-wave

velocity, δvp, and S-wave velocity, δvs, can be expressed as (Tan and Gurnis , 2007):

δvp =1

2

(

δK + 4R1δG/3

1 + 4R1/3− δρ

)

(2.12)

δvs =1

2(δG − δρ) (2.13)

19

Table 2.1: Generic model parametersParameter Symbol Value Units Non-dim Value

Rayleigh number Ra - - 1.437 × 109

Dissipation number Di - - 1.95Surface temperature TS 300 K 0.081

Density ρ0 3930 kg m−3 1.0Thermal expansion coefficient α0 3.896 × 10−5 K−1 1.0

Temperature drop ∆T 3700 K 1.0Earth radius R0 6371 km 1.0

Gravity g0 9.81 m s−2 1.0Thermal diffusivity κ0 10−6 m2 s−1 1.0

Heat capacity c0 1250 J kg−1 K−1 1.0Reference viscosity η0 1.0 × 1021 Pa s 1.0

Cohesion a 246 kPa 1.0 × 104

Brittle yield stress gradient b 6.187 MPa km−1 1.6 × 109

Ductile yield stress σy 986 MPa 4.0 × 107

Phase Rayleigh number Rb - - 1.99 × 108

Phase transition temperature TΓ 2603 K 0.704Phase transition width d 10 km 1.5 × 10−3

Table 2.2: Model specific parameters. a Phase transition pressure (equivalent heightabove CMB in km). b Clapeyron slope (equivalent in MPa K−1). c Stable phase atCMB: Perovskite (Pv), post-Perovskite (pPv)

Model pΓa γb CMB phasec

S1 No phase transitionS2 0.403 (300) 0.114 (7.6) pPvS3 0.403 (300) 0.160 (10.6) PvS4 0.379 (450) 0.160 (10.6) pPvS5 0.426 (150) 0.160 (10.6) PvS6 0.426 (150) 0.114 (7.6) PvS7 0.438 (75) 0.114 (7.6) PvS8 0.445 (32) 0.200 (13.3) PvS9 0.410 (255) 0.200 (13.3) Pv

20

where K is the adiabatic bulk modulus, G shear modulus, ρ density, and R1 = G/K

is equal to 0.45, which is similar to PREM at 2700 km depth. δρ is computed directly

from the geodynamic calculations (Appendix A). The perturbations to the elastic

moduli are decomposed into phase and thermal parts, assuming they are linearly

independent:

δK(Γ, T ) =∂lnK

∂ΓΓ +

∂lnK

∂TdT (2.14)

δG(Γ, T ) =∂lnG

∂ΓΓ +

∂lnG

∂TdT (2.15)

where dT is a temperature perturbation relative to a reference adiabat. We derive the

reference adiabat semi-empirically by considering the horizontally averaged tempera-

ture field for the models with a phase transition (Fig. 2.1). Since a phase transition

with a positive Clapeyron slope enhances convection we exclude the model without a

phase transition because the adiabatic temperature gradient is less steep and the ther-

mal boundary layers thicker, although the differences are not significant. We construct

a reference adiabat with a foot temperature of 0.49 (dimensionally 1700 K) using the

dissipation number and thermal expansion profile defined for the geodynamic calcula-

tions. These temperatures are contained within the range of time-average geotherms

from the models (grey region in Fig. 2.1) between 500 and 2250 km depth. Temper-

ature perturbations are then determined by removing the reference adiabat from the

computed temperatures.

We use ∂lnK/∂T = −0.1217 and ∂lnG/∂T = −0.319 derived from a theoretical

calculation for MgSiO3 (Oganov et al., 2001). However, we apply these values to both

21

0

500

1000

1500

2000

2500

dep

th (

km

)

0.25 0.50 0.75

temp

ref. adiabat

Figure 2.1: Geotherms and reference adiabat. Time-average geotherms (horizontallyaveraged temperature) of models with a phase transition are contained within thegrey region. The reference adiabat is illustrated with a black solid line.

the Pv and pPv phase. Note that these derivatives are non-dimensional because T is

a non-dimensional temperature.

Across the Pv-pPv transition, we prescribe fractional changes in both the shear

wave and the compressional wave and compute the corresponding derivatives (Ap-

pendix A):

∂lnG

∂Γ= 2δvsΓ +

Rb

Raα0∆T (2.16)

∂lnK

∂Γ=(

2δvpΓ +Rb

Raα0∆T

)

(1 + 4R1/3) − 4R1/3∂lnG

∂Γ(2.17)

where δvsΓ and δvpΓ are fractional perturbations to the S- and P-wave velocity,

respectively, due to the pPv phase transition. Beneath the Cocos Plate the average

S-wave increase is approximately 2% (δvsΓ = 0.02) and the P-wave variation is a few

fractions of a percent (Hutko et al., 2008). For simplicity we assign δvp = 0. The 1-D

22

seismic model IASP91 (Kennett and Engdahl , 1991) converts velocity perturbations

to absolute values.

We generate synthetic seismograms using the WKM technique to resolve the SdS

triplication originating from high-velocity regions of D′′ (Ni et al., 2000). In this initial

study we trace rays through seismic models computed from 1-D temperature and

phase profiles extracted from the 2-D convection calculations. We select a Gaussian

source time function with 4 s duration and bandpass the synthetic data between 4

and 100 s.

2.5 Results

2.5.1 Overview of D′′ slab dynamics

We describe typical slab dynamics using model S2 (Fig. 2.2) as all models exhibit sim-

ilar behavior. The pPv phase boundary is 300 km above the CMB and the Clapeyron

slope is 7.6 MPa K−1. Initially, the upper boundary layer thickens and the CMB

region warms (Fig. 2.2A). The pPv region has constant thickness except where a

few thin stationary plumes emanate from the lower thermal boundary layer and the

phase boundary is perturbed to higher pressure. A slab forms from the upper ther-

mal boundary layer when the yield stress is exceeded; sometimes the downwelling is

generated by several instabilities that unite to form a dominant downwelling. As the

slab descends it warms through adiabatic and viscous heating in addition to diffusion.

Pre-existing plumes at the CMB are displaced laterally by the downwelling, such

23

as the plume at the tip of the slab (Fig. 2.2B). The cold slab geotherm (Fig. 2.2G,

black solid line) intersects the phase boundary (grey dashed line) at lower pressure

than ambient mantle, which warps the phase boundary upward producing a thick

pPv layer. Latent heat release acts to restore the phase boundary to its unperturbed

position and generate a body force that opposes the motion of the slab. However,

the amplitude of the thermal anomaly and phase boundary deflection from advected

temperature generate the dominant buoyancy forces that are largely unmodified by

latent heating.

The slab smothers the CMB, trapping a portion of hot mantle that begins to vig-

orously convect. During this period the temperature-dependent rheology causes the

slab to deform more easily as it warms. The trapped mantle accumulates buoyancy,

forming a plume that pushes up the overlying slab (Fig. 2.2C). As the hot upwelling

rises from the CMB it enters the Pv stability field which creates strong phase het-

erogeneity and provides additional positive buoyancy because it is surrounded by

pPv. However, latent heat absorption cools the plume and retards the deflection of

the phase boundary, although these effects appear negligible. The upwelling erupts

through the slab and suppresses the height of the phase boundary (Fig. 2.2D). The

upwelling loses its thermal buoyancy through adiabatic cooling and thus its temper-

ature anomaly (relative to the reference adiabat) decreases rapidly as it rises.

Secondary plumes form from patches of thickened boundary layer on either side of

the original upwelling (Fig. 2.2D). These also punch through the slab and entrain some

of the remaining cooler material to create patches of deformed slab separated by plume

24

conduits (Fig. 2.2E, but more clearly visible in Fig. 2.2O). A second downwelling

at the rightmost edge of the domain displaces these patches and thermal contrasts

create topography on top of the pPv layer. As heat diffuses into the slab the thermal

anomaly is eradicated and the pPv layer returns to uniform thickness punctuated by

a few plumes as in Fig. 2.2A. This process is aperiodic.

2.5.2 Overview of seismic wavespeed anomalies

We compute P- and S-wave velocity anomalies using the geodynamic data (Fig. 2.2)

assuming that the P-wave is unperturbed by the phase boundary (δvpΓ=0%) and the

S-wave experiences a step-wise increase in velocity (δvsΓ=2%) (Fig. 2.3). P and S

phases with similar paths in the lower mantle will therefore generate different wave-

form complexity. Furthermore, seismic profiles depend on the evolutionary stage of

the slab and its interaction with the thermal boundary layer and pPv phase transition

(Fig. 2.3).

At 0 Myr, the seismic profiles are largely unperturbed except for the pPv phase

boundary (Fig. 2.3P) and reduced basal velocity caused by the lower thermal bound-

ary layer. The slab introduces thermal heterogeneity that produces a strong seismic

gradient across its top surface (Fig. 2.3Q). This thickens the pPv layer and generates

a much steeper velocity gradient for the S-wave than just the pPv transition alone

(Fig. 2.3Q). In this region the wavespeed reduction above the CMB is also larger than

it would be without an overlying slab.

The growth of a plume beneath the slab produces four distinctive seismic velocity

25

2000

2500

-0.5 0.0 0.5

diff temp

0

1000

2000

-0.5 0.0 0.5

diff temp

2000

2500

0.5 1.0

temp

0

1000

2000

0.0 0.5 1.0

temp

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

A 0 Myr

B 671 Myr

C 871 Myr

D 921 Myr

E 1148 Myr

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

Figure 2.2: Representative evolution of a slab in D′′ (model S2). Each row representsa different time slice and given times are relative to the top row. (A–E) Tempera-ture, (K–O) differential temperature (reference adiabat removed). The pPv layer atthe CMB is contoured in black. Black solid and dashed lines represent profile loca-tions. (F–J) Temperature profiles for A–E at the profile locations, (P–T) differentialtemperature profiles for K–O. The grey solid line denotes the reference adiabat (zerodifferential temperature for K–O) and the grey dashed line shows the Pv-pPv phaseboundary.

26

2000

2500

7.0 7.5

vs (km/s)

0

1000

2000

-6 -3 0 3 6

δvs (%)

2000

2500

13.0 13.5 14.0

vp (km/s)

0

1000

2000

-3 -2 -1 0 1 2 3

δvp (%)

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

A 0 Myr

B 671 Myr

C 871 Myr

D 921 Myr

E 1148 Myr

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

Figure 2.3: P- and S-wave velocity to compare with Fig. 2.2 (model S2, δvpΓ=0%,δvsΓ=2%). (A–E) P-wave, (K–O) S-wave velocity anomaly. (F–J) P-wave velocityprofiles for A–E, (P–T) S-wave velocity profiles for K–O. The grey line denotes the1-D seismic model IASP91.

27

gradients (Figs. 2.3H,R). Across the top of the slab the gradient is positive and steep,

but wavespeeds rapidly decline in the plume due to temperature and phase (S-wave

only). Wavespeeds are consistently low in the plume with a gradient comparable to the

1-D model. The thermal boundary layer at the base of the mantle generates a second

negative velocity gradient, although the actual decrease in velocity is significantly less

than the transition from slab to plume.

When the plume punches through the slab the rising hot material suppresses

wavespeeds and generates seismic profiles similar to those at 0 Myr (compare

Figs. 2.3I,S with Figs. 2.3F,P). The plume head is surrounded by cooler remnant

slab which introduces a negative wavespeed gradient at 2100 km depth. Secondary

plumes develop in the lower thermal boundary layer and break apart the remnant slab.

Velocity profiles through a developing plume in the pPv stability field (Figs. 2.3J,T,

black solid line) exhibit a low negative gradient at the CMB. This contrasts to a Pv

plume otherwise within a pPv layer which produces a positive velocity gradient except

for the very base of the mantle (compare Figs. 2.3J,T with Figs. 2.3H,R, black solid

line). The neighboring blocks of cool deformed slab produce a sharp phase boundary

with relatively high wavespeeds (Figs. 2.3J,T, black dashed line). The lower thermal

boundary is suppressed beneath the slab, which generates a high negative velocity

gradient at the base.

28

2.5.3 Dynamic and seismic variations

Our models explore variations in the phase boundary height and Clapeyron slope.

Increasing the pPv transition pressure at fixed temperature is equivalent to reducing

the pPv transition temperature at a fixed pressure because the pPv stability field is

simply translated in P–T space.

The leftmost columns of Figs. 2.4 and 2.5 show models with an increased Clapey-

ron slope of 10.6 MPa K−1. Models S3, S4, and S5 have equivalent transition pressures

of 300 km, 450 km, and 150 km above the CMB, respectively. We show the S-wave

velocity but the perturbations to the P-wave are comparable except for the step-wise

increase due to the pPv phase transition. Model S3 (Figs. 2.4A,E,B,F) has a transi-

tion pressure of 300 km above the CMB which is the same as the “typical” model in

Section 2.5.1. However, the Clapeyron slope is larger so the stable phase at the CMB

is now Pv rather than pPv and plumes form at the CMB in the Pv stability field

(Figs. 2.4A,E, black solid line). This accentuates the wavespeed contrast with the

overlying cooler pPv by producing a lower velocity basal layer (compare Figs. 2.3O,T

with Figs. 2.5A,E, black solid line). Figs. 2.4A,E reveal lower boundary layer insta-

bilities at various stages of their life cycle. This includes thickening of the boundary

layer, plume detachment from the CMB, and eruption through the pPv layer with a

trailing conduit. Plume heads become Pv within the pPv layer. Seismic waves may

therefore sample all of this complexity within small ranges of azimuth or epicentral

distance. At later time, several plumes punch through the slab and generate separate

blocks of pPv that are surrounded at the base and edges by hot Pv (Figs. 2.4B,F).

29

2000

2500

−0.5 0.0 0.5

diff temp

0

1000

2000

0.0 0.5 1.0

temp

2000

2500

−0.5 0.0 0.5

diff temp

0

1000

2000

0.0 0.5 1.0

temp

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

A S3 0 Myr

300 km10.6 MPa K−1

B S3 116 Myr

300 km10.6 MPa K−1

C S4

450 km10.6 MPa K−1

D S5

150 km10.6 MPa K−1

E

F

G

H

I S8 0 Myr

32 km13.3 MPa K−1

J S8 40 Myr

32 km13.3 MPa K−1

K S8 906 Myr

32 km13.3 MPa K−1

L S7

75 km7.6 MPa K−1

M

N

O

P

Figure 2.4: D′′ dynamic outcomes from parameter variation. (A–D) and (I–L) Tem-perature. The pPv layer at the CMB is contoured in black and the phase transitionparameters (height above the CMB and Clapeyron slope) are given below each panel.Black solid and dashed lines represent profile locations. (E–H) and (M–P) correspondto differential temperature profiles at the profile locations for A–D and I–L, respec-tively. The grey solid line denotes the reference adiabat (defined zero) and the greydashed line shows the Pv-pPv phase boundary. Given times are relative to 0 Myr forthat particular model.

30

2000

2500

7.0 7.5

vs (km/s)

0

1000

2000

-6 -3 0 3 6

δvs (%)

2000

2500

7.0 7.5

vs (km/s)

0

1000

2000

-6 -3 0 3 6

δvs (%)

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

2000

2500

0

1000

2000

A S3 0 Myr

B S3 116 Myr

C S4

D S5

E

F

G

H

I S8 0 Myr

J S8 40 Myr

K S8 906 Myr

L S7

M

N

O

P

Figure 2.5: S-wave velocity to compare with Fig. 2.4 (δvpΓ=0%, δvsΓ=2%). (A–D)and (I–L) S-wave velocity perturbation. (E–H) and (M–P) corresponding S-wavevelocity at the profile locations for A–D and I–L, respectively. The grey solid linedenotes the 1-D seismic model IASP91.

31

Model S4 has a lower transition pressure than S3 (450 km versus 300 km) which

is equivalent to translating the phase boundary to higher temperature (Figs. 2.4C,G)

such that the stable phase at the CMB is pPv. Plumes form in the pPv stability field

and intersect the Pv-pPv phase boundary as they rise through D′′. This forms isolated

pockets of hot Pv within the pPv-dominated layer (Fig. 2.4G, black dashed line) which

causes multiple perturbations to the S-wave velocity (Fig. 2.5G, black dashed line).

The thermal profile crosses the phase boundary multiple times and is an example of

a “triple crossing” (Fig. 2.4G, black dashed line). Escaping plume heads also create

concave-up notches in the phase boundary at the top of D′′ (Figs. 2.4C,G, black solid

line). This is also observed in S2 (Figs. 2.2O,T) but is more noticeable here because

the Clapeyron slope is larger. The pPv layer has a smooth upper surface at longer

wavelength, which contrasts with models that produce distinct pPv blocks. However,

the layer is permeated by plumes that produce low-velocity regions extending radially

from the CMB.

Model S5 has a higher transition pressure than S3 (150 km versus 300 km above

the CMB) but behavior is comparable because both models facilitate a double crossing

for the average 1-D geotherm. However, perturbations to the phase boundary height

are more comparable to the ambient thickness of the pPv layer (Fig. 2.4D). Blocks of

pPv are more separate and there is relatively larger topography on their tops.

A larger Clapeyron slope (13.3 MPa K−1) enables greater lateral phase hetero-

geneity (Figs. 2.4I,J,K). In model S8, pPv only forms within cold slabs in D′′ because

the average 1-D geotherm is too warm to sustain a permanent pPv layer (Fig. 2.4I,M,

32

black solid line). For example, pPv occurs around the tip of a slab as it penetrates D′′

(Fig. 2.4I) causing substantial variations in phase boundary height (Figs. 2.4M,N).

Plumes can penetrate through older slabs whilst downwelling material continues to

accumulate nearby, which forms both regions of pPv blocks and a continuous layer

(Fig. 2.4K).

Finally, a folded slab at the CMB has considerable complexity. Two negative

temperature perturbations are generated by the uppermost and lowermost parts of

the slab fold with ambient material sandwiched between (Fig. 2.4L). The top of the

lowermost thermal anomaly accompanies the transition to pPv. These features are

clearly evident in the seismic profile (Fig. 2.5P, black dashed line). Seismic velocity

gradients are steeper in the cold regions, with the second perturbation accentuated

by the phase transition. The negative velocity gradient at the base of the mantle is

large because of the overlying slab and Pv is the stable phase at the CMB.

2.5.4 Waveform predictions

Thermal and phase heterogeneity produce wavespeed perturbations that can be ex-

plored through waveform modeling. We produce 1-D synthetic seismograms for the

S-wave velocity profiles in Figs. 2.3 and 2.5. First we overview basic features that are

necessary to interpret the synthetic data.

The seismograms are aligned on the IASP91-predicted S arrival and the triplicated

SdS phase arrives before ScS. IASP91 (grey seismograms) does not produce a SdS

arrival as it lacks a velocity discontinuity just above the CMB. The height of the

33

60

70

80E

pic

entr

al d

ista

nce

(d

egre

es)

60

70

80

Ep

icen

tral

dis

tan

ce (

deg

rees

)

-15 0 15 30 -15 0 15 30Time aligned on IASP91 S-wave (seconds)

-15 0 15 30

A

B

C

ScS

SdS

S(ab)

D

E

F

Figure 2.6: Synthetic seismograms (S-wave) for the reference model to compare withFig. 2.3. (A–F) Seismograms for the profiles in Figs. 2.3P–T, respectively, are in blackand IASP91 are in grey. The S-wave structure is shown inset (same as Figs. 2.3P–T,axes from 6.8 to 7.8 km/s and 2000 to 2890 km depth, grey line denotes IASP91,dark grey horizontal line denotes 300 km above the CMB).

34

60

70

80

Epic

entr

al d

ista

nce

(deg

rees

)

60

70

80

Epic

entr

al d

ista

nce

(deg

rees

)

−15 0 15 30 −15 0 15 30 −15 0 15 30 −15 0 15 30

A

B

C

D

E

F

G

H

Time aligned on IASP91 S−wave (seconds)

Figure 2.7: Synthetic seismograms (S-wave) for dynamic variations to compare withFig. 2.5. (A–B) Seismograms for the black solid and dashed profiles from Fig. 2.5E,respectively. Similarly for (C–D) Fig. 2.5F, (E–F) Fig. 2.5G, (G–H) Fig. 2.5H. SeeFig. 2.6 caption.

35

60

70

80

Epic

entr

al d

ista

nce

(deg

rees

)

60

70

80

Epic

entr

al d

ista

nce

(deg

rees

)

−15 0 15 30 −15 0 15 30 −15 0 15 30 −15 0 15 30

A

B

C

D

E

F

G

H

Time aligned on IASP91 S−wave (seconds)

Figure 2.8: Synthetic seismograms (S-wave) for dynamic variations to compare withFig. 2.5. (A–B) Seismograms for the black solid and dashed profiles from Fig. 2.5M,respectively. Similarly for (C–D) Fig. 2.5N, (E–F) Fig. 2.5O, (G–H) Fig. 2.5P. SeeFig. 2.6 caption.

36

interface can be determined by SdS-S and ScS–SdS differential travel times. For

a given epicentral distance, SdS–S increases and ScS–SdS decreases as the phase

boundary is perturbed to high pressure. The relative amplitude response of SdS

depends on the magnitude of the velocity increase across the discontinuity and ScS–

S constrains the volumetric velocity anomaly within D′′ (below the interface). SdS

overtakes S as the first arrival at post-crossover distances, which is ∼ 85 degrees

for the 1-D seismic model SLHO for a focal depth of 600 km (Lay and Helmberger ,

1983). A negative seismic velocity gradient above the CMB slows SdS which pushes

the post-crossover SdS and S arrivals together. Furthermore, more energy turns below

the discontinuity, which weakens the post-crossover S phase (Young and Lay , 1987).

A recently subducted slab produces a large velocity increase at the phase boundary

because of the coincident strong thermal gradient and phase jump (Fig. 2.3L) which

generates large SdS amplitude (Fig. 2.6B). Conversely, for a slab that has warmed at

the CMB the thermally induced velocity jump at the D′′ discontinuity is less and the

SdS amplitude is reduced (Fig. 2.6E). Relative to a thinner D′′ region, a slab with a

broad thermal anomaly elevates the phase boundary, which causes SdS to appear at

shorter distances, decreases SdS–S, and reduces the SdS–S crossover distance (com-

pare Fig. 2.6B with Fig. 2.6E). Thick D′′ regions with cold slabs have a large positive

volumetric wavespeed anomaly which causes ScS to arrive early (ScS–S decreases)

and therefore reduces the ScS–S crossover distance (Fig. 2.6B). As D′′ becomes in-

creasingly thin, ScS arrives closer to the IASP91 prediction, SdS–S increases, and

ScS–SdS decreases until SdS arrives as a precusory shoulder to ScS (Figs. 2.8D,E).

37

Post-crossover SdS amplitude is large for fast regions that extend from the phase

boundary to the CMB (e.g., Fig. 2.6B).

A thickening boundary layer at the base of a slab has a negative wavespeed

anomaly which increases the arrival time of ScS (ScS–S increases) by reducing the

volumetric wavespeed anomaly (Fig. 2.6F). As a plume develops, the wavespeeds be-

neath the D′′ discontinuity continue to decrease and ScS arrives with the IASP91

prediction (Fig. 2.7G) or is delayed (Fig. 2.6C and Fig. 2.7B). These results are

consistent with the volumetric velocity anomaly controlling ScS–S travel times (e.g.,

Sidorin et al., 1999a). The temperature anomaly at the phase interface decreases as

the plume heats the overlying slab, which reduces SdS amplitude by decreasing the

velocity jump (Fig. 2.7C). However, SdS–S does not vary because this is sensitive to

the height of the discontinuity above the CMB, which is unaffected by plume growth

within D′′ until the plume erupts through the phase boundary. A warm plume bends

rays away from the normal which reduces S and SdS amplitude beyond the SdS–S

crossover relative to a horizontal slab (compare Fig. 2.7G and Fig. 2.7H beyond ∼ 80

degrees).

Fig. 2.7F shows the seismogram for a Pv plume head within a pPv layer (Fig. 2.4C,

black dashed line). SdS arrives from the top of the pPv layer but a second triplicated

arrival from the warm plume to pPv transition at higher pressure is absent. The

slow velocity within the plume presumably creates a shadow zone that suppresses

this second arrival. The waveforms for this profile are similar to those produced by

a simple phase transition overlying a thermal boundary layer (Fig. 2.7A). Although

38

the velocity structure differs from IASP91, the arrival time of S and ScS is similar.

The seismogram for a plume erupting through a pPv layer has an additional (weak)

triplication phase that arrives after S for distances 60–68 degrees (Fig. 2.6D). This

phase originates from cooler slab material carried above the plume head. Beyond 75

degrees the direct S arrival enters a shadow zone due to ray bending from sampling

the slower velocity plume. Since the wavespeed anomalies are generally negative

throughout D′′, the SdS–S and ScS–S crossover distances are > 84 degrees. Two

triplicated arrivals are also produced by a folded slab interacting with the phase

transition (Figs. 2.4L,2.5L). The first arrives between 62–70 degrees and originates

from the top of the uppermost slab fold (Fig. 2.8H). The second arrives beyond 65

degrees and is SdS from the velocity increase caused by the slab interacting with the

phase boundary. Combined analysis of multiple triplicated arrivals, possibly with

other phases, may be able to determine the characteristic lengthscale of slab folding

above the CMB.

A simple thermal boundary layer at the CMB delays ScS, and marginally delays

the arrival time for S at large distances (> 80 degrees) (Figs. 2.8A,F). A warm conduit

emanating from the CMB delays S beginning at shorter distances (> 76 degrees) and

further suppresses the amplitude of the arrival (Fig. 2.6A). Additionally, a weak

SdS phase is faintly visible beyond about 72 degrees and is generated by the small

velocity increase at the phase transition (Fig. 2.6A). ScS–SdS is small because the

discontinuity is close to the CMB.

39

2.6 Discussion

Slabs rapidly advect and blanket the CMB from episodic flushing of the upper ther-

mal boundary layer. The maximum thermal anomaly of slabs at the CMB is 0.33

(1200 K), which is at the upper bound of estimates (Steinbach and Yuen, 1994).

Additionally, the simple two-phase model (Pv and pPv) and uncertainties in mate-

rial properties preclude an accurate mapping of temperature and phase to seismic

wavespeed. However, we focus on changes in seismic velocity gradient because the

absolute magnitude of velocity perturbation is not critical for analyzing trends in

seismic triplication data. Similarly, choosing an alternative reference geotherm would

not significantly affect our results. The largest discrepancy between the horizontally

averaged temperature and reference adiabat is in the region of subadiabatic temper-

ature gradients above the CMB. If we choose a horizontally averaged temperature

as reference (extrapolating across the boundary layers) the wavespeed anomaly for

slabs (plumes) will slightly decrease (increase) in amplitude. Finally, diffuse ther-

mal anomalies at the CMB would not produce sharp seismic gradients and lateral

variation in the phase boundary necessary to investigate high-frequency waveform

complexity.

Downwellings displace pre-existing plumes at the CMB because low-viscosity con-

duits are established between subduction cycles. Therefore plumes infrequently de-

velop at slab tips in comparison to models with an unperturbed lower thermal bound-

ary layer (Sidorin et al., 1998; Tan et al., 2002). Episodic subduction promotes plume

development beneath slabs because existing basal instabilities are swept aside. Slabs

40

insulate the CMB allowing the boundary layer to thicken and form upwellings. Tan

et al. (2002) investigate these dynamics and propose two types of outcomes: “normal

plumes” and “mega-plumes”. Qualitatively the plumes that we observe are more akin

to “normal plumes” because they are not voluminous eruptions and dissipate quickly

above the CMB. We anticipate different behavior because our models are compress-

ible with a phase transition, whereas the fine-scale models of Tan et al. (2002) are

Boussinesq. Convective vigor and adiabatic cooling control the temperature anomaly

of plumes in compressible flow models (Zhao and Yuen, 1987). After plumes dissipate

the thermal anomaly of the slab they combine into a few single upwellings (Vincent

and Yuen, 1988).

Nevertheless, the seismic profile for a mega-plume beneath an ancient slab (Fig. 11,

right panel in Tan et al., 2002) is comparable to a plume within a pPv layer (e.g.,

Fig. 2.3M,R). The later includes an S-wave velocity increase across the Pv-pPv phase

boundary. Uncertainties when mapping temperature and phase to seismic wavespeed

prevent 1-D seismic analyses from identifying a warm plume (seismically slow) versus

a hot mega-plume (slower). Furthermore, we extract 1-D temperature and phase

profiles from 2-D convection calculations and are therefore insensitive to the total

volume of the plume. The profiles above the CMB are different because Tan et al.

(2002) compute δvs using the horizontally averaged temperature field as a reference

geotherm, whereas we use an adiabat. Our models therefore include a negative seismic

velocity gradient just above the CMB in accordance with seismic data (Cleary , 1974).

The models suggest several mechanisms that may explain the origin of some seis-

41

mic scatterers. First are small-scale plumes at different stages of development forming

in a pPv layer (Fig. 2.4A). The phase difference between a Pv plume and the sur-

rounding pPv layer will further increase wavespeed variations in comparison to just

the temperature effect. Second are steep-sided isolated blocks of pPv (Fig. 2.4B).

Third are concave-up notches in the phase boundary caused by escaping plume heads

(Fig. 2.4C). Furthermore, these processes often operate in combination.

The synthetic seismograms reveal triplicated arrivals originating from the D′′ dis-

continuity and large thermal gradients, e.g., a folded slab (Fig. 2.8H). The timing and

amplitude response of the arrivals provide insight into the velocity increase, height of

the phase transition above the CMB, and approximate thickness of the fast region.

However, S, SdS and ScS in the distance range 60–83 degrees are largely insensitive

to small-scale features beneath the phase boundary. Negative seismic gradients are

inherently difficult to resolve because energy is not refracted to the surface, which

means that low-amplitude reflected arrivals, often below the noise level, have to be

analyzed (e.g., Flores and Lay , 2005). The ScS–S differential travel time constrains

the volumetric wavespeed anomaly of D′′ but is not sensitive to the distribution of

heterogeneity.

2.7 Conclusions

The models reveal complex interaction of slabs, plumes, and the Pv-pPv transition

which produces significant thermal and phase heterogeneity in D′′ over small distances.

Slabs deflect the phase boundary and disturb the lower thermal boundary layer,

42

pushing aside pre-existing upwellings. Plumes regularly develop beneath slabs and

distort the phase boundary and slab morphology as they erupt from the CMB. Plume

formation occurs less frequently at slab edges because a few stationary upwellings

drain the boundary layer between cycles of subduction. Advected isotherms produce

more complicated thermal structure than conductive profiles. This enables multiple

crossings of the phase boundary, e.g., a Pv plume head within a pPv layer can produce

a “triple crossing”.

The topology of the pPv layer depends on the transition pressure (or equivalently

transition temperature since both translate the phase boundary in P–T space) and the

Clapeyron slope. The models reveal a variety of behavior including: (1) distinct pPv

blocks separated by upwellings, (2) notches at the top of a pPv layer caused by plume

heads, (3) regions of Pv embedded within a pPv layer due to upwellings. Furthermore,

these scenerios have interesting consequences for seismic scattering phenomena which

will be explored in a future study.

In synthetic seismograms, we cannot resolve small-scale complexity beneath the

D′′ discontinuity using solely S, SdS, and ScS triplication data to 84 degrees. This

is because of inherent limitations in resolving negative seismic velocity gradients. In

future work we will model the seismic wavefield using a finite difference approach to

explore SH-, SV-, and P-waves for many D′′ arrivals (e.g., S, Scd, ScS, SKS, SKKS)

and potentially reverberations in the pPv layer. Extending the distance range to 110

degrees will also allow us to analyze diffracted phases (e.g., Sd) and arrivals beyond

the SdS–S crossover distance. 2-D models can explore the focusing and defocusing

43

of seismic rays due to topography on the phase boundary, and the effects of seismic

anisotropy also need evaluating.

There are possibilities for developing more complex dynamic models. Composi-

tionally stratified slabs, possibly interacting with a chemical layer at the CMB, will

also generate waveform complexity (Tackley , 2011). Furthermore, chemical hetero-

geneity in D′′ influences seismic velocities and the Pv-pPv transition pressure and

depth of the mixed phase region. Thermal conductivity strongly controls heat trans-

port at the CMB and therefore the thermal evolution of slabs.

44

Chapter 3

A geodynamic and mineral physics

model of a solid-state

ultralow-velocity zone

Originally published in:

Bower, D. J., J. K. Wicks, M. Gurnis, and J. M. Jackson (2011), A geo-dynamic and mineral physics model of a solid-state ultralow-velocity zone,Earth Planet. Sc. Lett., 303, 193–202, doi:10.1016/j.epsl.2010.12.035.

3.1 Abstract

Recent results (Wicks et al., 2010) suggest that a mixture of iron-enriched (Mg,Fe)O

and ambient mantle is consistent with wavespeed reductions and density increases in-

ferred for ultralow-velocity zones (ULVZs). We explore this hypothesis by simulating

convection to deduce the stability and morphology of such chemically distinct struc-

tures. The buoyancy number, or chemical density anomaly, largely dictates ULVZ

shape, and the prescribed initial thickness (proxy for volume) of the chemically dis-

tinct layer controls its size. We synthesize our dynamic results with a Voigt-Reuss-Hill

mixing model to provide insight into the inherent seismic trade-off between ULVZ

thickness and wavespeed reduction. Seismic data are compatible with a solid-state

45

origin for ULVZs, and a suite of these structures may scatter seismic energy to produce

broadband PKP precursors.

3.2 Introduction

The large chemical, density, and dynamical contrasts associated with the juxtapo-

sition of liquid iron-dominant alloy and solid silicates at the core-mantle boundary

(CMB) are associated with a rich range of complex seismological features. Seismic

heterogeneity at this boundary includes small patches of anomalously low sound ve-

locities, called ultralow-velocity zones (ULVZs). Their small size (5 to 40 km thick)

(e.g., Garnero and Helmberger , 1996) and depth (> 2800 km) present unique chal-

lenges for seismic characterization.

ULVZs were first noted with teleseismic SPdKS phase diffracting along the CMB

to determine the P-wave velocity at the base of the mantle beneath the central Pacific

(e.g., Garnero et al., 1993b; Garnero and Helmberger , 1995, 1996; Helmberger et al.,

1996). The compressional wavespeed decreases by 5 to 10% over a depth of 5 to

40 km above the CMB, consistent with PcP precursors (e.g., Mori and Helmberger ,

1995; Revenaugh and Meyer , 1997; Hutko et al., 2009). In other locations, ULVZs are

seismically absent or below the detection threshold, such as the North Pacific (Rost

et al., 2010a), which may imply they are not globally ubiquitous (see Thorne and

Garnero, 2004). ULVZs have been correlated with the location of hotspots (Williams

et al., 1998) and tentatively to the edges of large low-shear velocity provinces (e.g.,

Lay et al., 2006). Recent thermochemical convection calculations lend support to

46

these spatial correlations (McNamara et al., 2010).

Precursors and postcursors to the converted core-reflected phase ScP can poten-

tially constrain the P and S wavespeed, thickness, and density of ULVZs (e.g., Garnero

and Vidale, 1999; Reasoner and Revenaugh, 2000). Based on this approach, analyses

using small-aperature and short-period arrays have elucidated the structure between

Tonga–Fiji and Australia at high resolution (Rost and Revenaugh, 2003; Rost et al.,

2005, 2006; Idehara et al., 2007; Rost et al., 2010b). These studies report P and S

wavespeed reductions of ≈ 8% and ≈ 24%, respectively, a thickness of about 10 km,

and a density increase of around 10%.

All of these studies characterize structure with a 1-D model. Although quasi-1D

models utilize different structures for the source and receiver paths (e.g., Garnero and

Helmberger , 1996; Helmberger et al., 1996), only a few 2-D models have been reported.

Probing the CMB beneath the southwest Pacific, Wen and Helmberger (1998a) model

SKS-SPdKS observations with Gaussian-shaped ULVZs of approximately 40 km in

height, 250 to 400 km lateral extent, and a P-wavespeed drop of about 10%. PKP

precursors suggest that these larger structures are composed of smaller undulations

(Wen and Helmberger , 1998b). A concave-down upper interface is necessary to model

structures beneath Africa and the eastern Atlantic (Helmberger et al., 2000). In both

1-D and 2-D models there are trade-offs between the height and velocity decrease of

ULVZs (e.g., Garnero and Helmberger , 1998; Wen and Helmberger , 1998a).

A partial-melt origin for the ULVZs predicts a P-to-S wavespeed reduction of

about 1:3 (Williams and Garnero, 1996; Berryman, 2000; Hier-Majumder , 2008). In

47

this model, the velocities of the average assemblage are decreased by melt formed ei-

ther by fluid reaction products of Fe liquid with silicate mantle or by partial melting

of Fe-rich mantle. The hypothesis is consistent with the correlation between ULVZs

and hot spots (Williams et al., 1998) and the broad agreement with P-to-S veloc-

ity reductions determined from core-reflected phases. Early dynamical calculations

question the ability to produce a dense and non-percolating melt phase in the deep

Earth (Hernlund and Tackley , 2007). However, the stirring of ULVZs by the larger-

scale convective motions of the mantle can potentially maintain a partially molten

region (Hernlund and Jellinek , 2010). Partial melt may also be trapped within ULVZs

because of textural changes (e.g., Rost et al., 2005, 2006), but theoretical and exper-

imental justifications are incomplete, particularly at the temperatures and pressures

of the CMB region.

Iron enrichment of solid phases, specifically the increase in Fe/(Fe+Mg) ratio, can

simultaneously increase density and reduce compressional and shear velocity (e.g.,

Karato and Karki , 2001). This partly inspired the notion of solid, iron-rich ULVZs,

such as a metal-bearing layer (Knittle and Jeanloz , 1991; Manga and Jeanloz , 1996),

subducted banded iron formations (Dobson and Brodholt , 2005), or iron-enriched

post-perovskite (Mao et al., 2006; Stackhouse and Brodholt , 2008). Iron-rich systems

are typically denser than the surrounding mantle, which is required to explain the

locations of ULVZs at the base of the mantle.

Recent results show that the sound velocities of a solid iron-enriched (Mg,Fe)O at

CMB pressures are low enough, such that only a volumetrically small amount (∼ 10–

48

20%) mixed with coexisting silicates are needed to explain ULVZs (Wicks et al., 2010).

We are motivated to generate a numerical convection model of a thin, iron-enriched

(Mg,Fe)O-containing layer interacting with the lowermost thermal boundary layer.

Mantle convection thickens (thins) a dense layer beneath upwellings (downwellings)

and controls its spatial distribution (Davies and Gurnis , 1986). A persistent stable

layer has a density contrast of a few percent (e.g., Garnero and McNamara, 2008)

and may convect internally (Hansen and Yuen, 1988). We explore whether these

characteristics are manifested in this iron-enriched (Mg,Fe)O-containing layer. We

determine the steady-state morphology of such a layer and develop an integrated and

self-consistent ULVZ model which uses constraints from geodynamics and mineral

physics and is consistent with seismic data.

3.3 Numerical models

3.3.1 Equations and solution methods

We apply the Boussinesq approximation to model thermochemical convection using

CitcomS (Zhong et al., 2000; Tan et al., 2007) because the pressure range of our

domain is small and energy dissipation is negligible with a greatly reduced thermal

expansion coefficient at high pressure. The equation for the conservation of mass for

an incompressible fluid is:

∇ · u = 0 (3.1)

49

where u is velocity. The non-dimensional momentum equation is:

−∇P + ∇ · (ηǫ) = (RbC − RaT )r (3.2)

where P is the dynamic pressure, η is the viscosity, ǫ is the deviatoric strain rate,

Ra is the thermal Rayleigh number, T is temperature (non-dimensionally ranging

from 0 to 1), Rb is the chemical Rayleigh number, and r is the radial unit vector.

Composition, C, ranging from 0 to 1, encompasses two chemical components. The

first component (C = 0) is ambient mantle, the second (C = 1) is a two-phase

mix containing iron-enriched (Mg,Fe)O that constitutes the distinct chemistry of the

ULVZ. We equivalently refer to the latter component as the chemical, or (Mg,Fe)O-

containing, component.

The Rayleigh numbers are defined as:

Ra =ρα∆TD3g

η0κ(3.3)

Rb =∆ρchD

3g

η0κ(3.4)

where the parameters and their values are provided in Table 3.1. A useful non-

dimensional parameter is the buoyancy number, B, which describes the chemical

density anomaly normalized by the maximum thermal density anomaly, or equiva-

lently the ratio of chemical-to-thermal buoyancy:

B =Rb

Ra=

∆ρch

ρα∆T. (3.5)

50

Table 3.1: Model parametersParameter Symbol Value UnitsDensity ρ 5500 kg m−3

Thermal expansion coefficient α 10−5 K−1

Temperature drop ∆T 1500 KMantle depth D 2890 km

Gravity g 10.3 m s−2

Thermal diffusivity κ 10−6 m2s−1

Reference viscosity η0 1022 Pa sViscosity exponent q 3 -

Thermal Rayleigh number Ra 2 × 106 -Thermal boundary layer initial thickness dt 66 km

Buoyancy number B 0.5, 0.75, 1, 1.25, 2, 4, 6 -Chemical density ∆ρch Bρα∆T kg m−3

Chemical Rayleigh number Rb BRa -Chemical layer initial thickness dch 2, 4, 8, 16, 24, 32 km

The quantity of heat-producing elements in the lower mantle and the dynamic im-

plications for small-scale structures such as ULVZs remain uncertain. For simplicity,

we solve the non-dimensional energy equation for temperature without an internal

heat source:

∂T

∂t+ (u · ∇)T = ∇2T (3.6)

where t is time.

The equation for chemical advection is:

∂C

∂t+ (u · ∇)C = 0. (3.7)

We represent the ULVZ component by a set of tracer particles (initially about 100/cell)

that are advected using a predictor-corrector scheme (McNamara and Zhong , 2004).

The volume fraction of ULVZ material is proportional to the absolute local concen-

51

tration of tracers with a truncation applied to prevent unphysically large values (see

Tackley and King , 2003, the truncated absolute method). In comparison to the ra-

tio method (Tackley and King , 2003), this technique provides greater computational

speed because fewer total tracers are required. Although the number of tracers per

cell is greater for the absolute method to achieve the same resolution, a large volume

fraction of ambient material in our models is devoid of tracers. By contrast, the ratio

method requires tracers to fill the space of the entire domain.

3.3.2 Domain and rheology

We solve for the flow within a small region near the CMB in a cylindrical geometry.

Our domain (513×145 nodes) spans approximately 23◦ with a height of 488 kilometers

above the CMB. The radial resolution is 2 km in the lowermost 256 km of the domain.

Above 256 km the grid spacing increases incrementally by 2 km to a maximum of 20

km.

Non-dimensional viscosity (normalized by η0, see Table 3.1) follows a linearized

Arrhenius law; recalling that T is non-dimensional temperature:

η(T ) = exp(− ln(10q)T ) (3.8)

where q specifies the order of magnitude of viscosity variation within the domain (see

Table 3.1) and is largely restricted by numerical considerations. The stability of the

lower thermal boundary layer is strongly dependent on q (e.g., Yuen and Peltier ,

1980; Loper and Eltayeb, 1986). The background viscosity modulates the critical size

52

that an instability must attain before a diapir can detach from the thermal boundary

layer (e.g., Olson et al., 1987). Therefore, the reference viscosity η0 (see Table 3.1) is

representative of the unperturbed ambient mantle beyond the influence of the thermal

boundary layer.

3.3.3 Boundary and initial conditions

The comparatively large lateral extent of the domain limits the sensitivity of the

solution to the insulating sidewalls. The bottom boundary (CMB) is isothermal and

free slip. We apply two different top boundary conditions. An isothermal and free-

slip condition (impermeable) excessively constrains flow and retards upwellings. In

contrast, a boundary prescribed by zero normal stress, zero horizontal velocities, and

zero heat flux (permeable) (e.g., Tan et al., 2002) lessens resistance so that instability

growth accelerates. The impermeable and permeable conditions effectively bound the

characteristic dynamic timescales that we expect for an evolving thin boundary at

the base of a thick domain (Olson et al., 1987).

Ambient deep mantle is prescribed at zero (non-dimensional) temperature, and

the isothermal lower boundary is set to unity. The temperature scaling is given in

Table 3.1. We apply a half-space cooling model with an age of 25 Myr to generate

a lower thermal boundary layer with a thickness of ≈ 66 km. We place a thin layer

of the chemical component at the base within the thermal boundary layer. Both the

buoyancy number (B) and initial thickness (dch) are free parameters (see Table 3.1).

We explore cases where dch ranges from 32 km to 2 km, which is between 2 and 33

53

times smaller than the initial thermal thickness. This is reasonable given the expected

thickness (5–40 km) of ULVZs.

We allow the chemical layer to be swept into one coherent structure by applying

a half-sinusoidal perturbation to the temperature field (initially of non-dimensional

magnitude of 0.05) both radially and laterally. This permits the outcome of the

different numerical experiments to be compared more readily. The size of our domain

is carefully specified to focus on individual ULVZ structures and is not designed (nor

suitable) to analyze the spatial distribution of many piles. Physically, our chosen

initial perturbation is akin to an upwelling on the CMB caused by the (symmetric)

downwelling of ambient material on either side.

3.4 Results

3.4.1 Transient period

We refer to the initial stage of the model evolution as the transient period. Although

we are primarily concerned with the long-term stability and morphology of ULVZs,

during this time we make several observations. We overview the evolution of four

extreme cases (all impermeable), given by the following parameter values: (B =

0.5, dch = 16 km), (B = 4, dch = 16 km), (B = 0.5, dch = 8 km), and (B = 4, dch =

8 km).

For (B = 0.5, dch = 16 km) (Fig. 3.1), the thermal boundary layer develops two

dominant instabilities within the chemical layer (Fig. 3.1A) that are ultimately over-

54

whelmed by the imposed long-wavelength perturbation (Fig. 3.1B). During this pe-

riod, the chemical layer develops significant relief caused by the developing plumes,

until the plumes merge and a large volume fraction of the layer is expelled from the

CMB region (Fig. 3.1C). The buoyancy of the plume generates viscous stresses that

support the relief of the remaining chemical material anchored at the CMB. Stresses

reduce as the plume ascends away from the lower boundary and the convection ap-

proaches a steady state, causing a marginal reduction in relief.

The evolution for the case with the same buoyancy number, but a thinner layer

(B = 0.5, dch = 8 km) is similar, but the dynamic timescale is reduced by several tens

of million years. This occurs for all cases with a thinner layer, because less thermal

buoyancy (less thickening of the boundary layer) is necessary to overcome the intrinsic

density increase of the chemical layer.

For the cases with a large chemical density anomaly, (B = 4, dch = 16 km) and

(B = 4, dch = 8 km), a single plume forms that marginally deflects the layer upward

as it leaves the CMB region. The influence of the buoyant plume is lessened as it

approaches the top of the domain, which causes the layer to flatten slightly. The

large chemical density anomaly prevents substantial topography from forming on the

interface.

3.4.2 Steady state

After the initial transient period, the low effective Rayleigh number ensures that

almost all models reach a steady state, defined by < 1 km fluctuations (standard

55

0˚5˚ 10˚ 15˚ 20˚

2400

2500

2600

2700

2800

0˚5˚ 10˚ 15˚ 20˚

2400

2500

2600

2700

2800

0˚5˚ 10˚ 15˚ 20˚

2400

2500

2600

2700

2800

CMB-1500K CMB

Temperature

Dep

th (

km

)D

epth

(km

)D

epth

(km

)

65 Myr

75 Myr

86 Myr

A

B

C

Figure 3.1: Representative behavior during the transient period for a model witha low chemical density anomaly and hence entrainment (B = 0.5, dch = 16 km,impermeable domain). The ULVZ component is contained within the area outlinedin green and the CMB.

56

deviation) in structure height. We can thus determine several time-independent

characteristics. We record the layer dimensions for the impermeable cases during

a steady-state time window defined after the plume reaches the top of the domain

but before the downwellings exert sufficient stress to further deform the chemical

layer. The permeable cases are unaffected by return flow because material is allowed

to escape from the domain.

Five impermeable cases are time-dependent because of an oscillatory flow driven

by a pulsating plume that marginally raises and flattens the chemical structure. We

compute the standard deviation of the maximum height (km), hsd, during a stationary

time window: (B = 0.5, dch = 2 km): hsd = 5.8 km, (B = 0.5, dch = 4 km): hsd = 2.6

km, (B = 0.75, dch = 2 km): hsd = 1.9 km, (B = 0.75, dch = 4 km): hsd = 1.1

km and (B = 1, dch = 2 km): hsd = 1.5 km. These models are characterized by a

low buoyancy number and low initial layer thickness such that the buoyancy of the

chemical layer is insufficient to stabilize the flow. We time-average these cases to

deduce the stationary steady-state behavior.

Fig. 3.2 depicts all of our parameter space. The relief is defined as the difference

between the maximum and minimum height of the structures above the CMB over

the lengthscale of the domain (∼ 1400 km) at steady-state. This metric becomes less

appropriate for cases where the ULVZ spreads over a distance greater than 1400 km,

thus creating a ubiquitous layer with a much reduced relief even though a potentially

voluminous layer exists. Although this may not occur within a larger model domain, a

thick continuous layer does not satisfy the small-scale localized nature of the ULVZs.

57

The two largest initial chemical layer thicknesses, dch = 32 km and dch = 24 km,

generally produce thick ubiquitous layers, or structures with reliefs that are too large

to reconcile with seismic observations (i.e., & 100 km). We therefore do not discuss

these results further.

A certain volume of residual material is necessary to generate structural reliefs

within the seismic estimates of 5–40 km. In these models, this can be achieved

by either entraining a large amount of material from a thicker chemical layer e.g.,

(B = 0.5, dch = 16 km), or by starting with less material, e.g., (B = 0.75, dch = 4 km).

We plot the steady-state morphologies for the impermeable and permeable cases

in Figs. 3.3, 3.4, and 3.5. Although the dynamic timescales are affected by the top

boundary condition, the long-term evolution of the structures is comparable. Models

with low B exhibit triangular morphologies and these shapes progressively flatten as

B is increased, with the upper interface becoming more rounded. The morphologies

are relatively insensitive to dch, although for reduced dch the structures exhibit slightly

flatter tops (e.g., Fig. 3.3)

Entrainment modulates the quantity of material available to form the structures

for B . 0.75. For dch ≥ 8 km a large volume fraction of the chemical layer is en-

trained when B = 0.5, which explains the substantially reduced size of the triangular

ULVZs. This effect is accentuated for the impermeable cases because of increased

viscous stresses. Entrainment is most effective at early model time because viscosi-

ties and density differences are comparable (e.g., Sleep, 1988). For this reason, the

thinnest initial layer is less affected because it is deeply embedded in the hottest,

58

Init

ial

chem

ical

lay

er t

hic

knes

s (k

m)

0 1 2 3 4 5 6

Buoyancy number

0

50

100

150

200

32

24

16

8

4

2

Relief(km)

Entrainment No entrainment Ubiquitous layer

Figure 3.2: Relief of the structures at steady state. For each initial chemical layerthickness, datapoints corresponding to the impermeable cases are located above thepoints for the permeable cases. “Ubiquitous layer” refers to cases where the chemicallayer occupies the full lateral extent of the domain.

59

Init

ial

chem

ical

lay

er t

hic

kn

ess

(km

)

0 1 2 3 4 5 6

Buoyancy number

0

20

40

60

80

100

120

16

8

4

2

Relief(km)

Entrainment No entrainment Ubiquitous layer

100 km

Figure 3.3: Relief of the structures at steady state. The morphologies for B = 0.5to B = 4, plotted to scale, are shown in successive order from left to right abovetheir corresponding datapoints. For B = 6 the morphologies are omitted because ofspace consideration but are comparable to B = 4. Permeable cases: black outline,impermeable cases: black fill. Note color scale is different in Fig. 3.2.

60

Init

ial

chem

ical

lay

er t

hic

kn

ess

(km

)

0 1 2 3 4 5 6

Buoyancy number

0

100

200

300

400

500

600

700

16

8

4

2

Half-width(km)

Entrainment No entrainment Ubiquitous layer

100 km

Figure 3.4: Half-width of the structures at steady state. See Fig. 3.3 caption forlegend.

61

Init

ial

chem

ical

lay

er t

hic

kn

ess

(km

)

0 1 2 3 4 5 6

Buoyancy number

0.00

0.25

0.50

0.75

1.00

16

8

4

2

AspectRatio

Entrainment No entrainment Ubiquitous layer

100 km

Figure 3.5: Aspect ratio (relief/half-width) of the structures at steady state. SeeFig. 3.3 caption for legend.

62

least viscous part of the domain. Lin and van Keken (2006) describe the entrainment

as end-member regimes, which can conveniently be applied to our models. In their

regime I, the plume head is formed by ambient material above the CMB, and no

chemically distinct material is entrained. This occurs for B & 0.75 in our models.

B . 0.75 is characteristic of their regime III, particularly for dch ≥ 8 km, because

the dense component predominantly accumulates at the base of the plume with some

entrainment by the plume head. In addition to this complex entrainment behav-

ior, relief varies most greatly around B = 1 because of the comparable thermal and

chemical buoyancy (Fig. 3.3).

The half-widths of the structures vary in proportion to B (Fig. 3.4). Since dch

limits the total volume of material available to form the ULVZ, the half-width also

varies in proportion to dch. For B & 0.75 the permeable cases produce structures that

are slightly less flattened than the impermeable cases, with a subsequent reduction in

half-width. The largest variations for both half-widths and relief occur for the thickest

initial layer, dch = 16 km. In Fig. 3.5 we show that the aspect ratio (relief/half-width)

of the structures is strongly dependent on B and only marginally dependent on dch.

3.5 Discussion

PKP precursors provide evidence for scatterers of varying lengthscales at the CMB

(Cleary and Haddon, 1972). Our simulations generate structures of various shapes

and sizes (e.g., Fig 3.3) which are comparable to the small-scale and large-scale fea-

tures used to model broadband data (Wen and Helmberger , 1998b). This suggests

63

that solid-state ULVZs are strong candidates for the origin of the scatterers, partic-

ularly if dynamic processes sweep together several ULVZs of differing lengthscales.

Many of our dynamic structures also have concave-down upper surfaces that are akin

to the 2-D Gaussian shapes used to model seismic data (e.g., Wen and Helmberger ,

1998b,a). A curved surface generates long-period PKP precursors by wide-angle re-

flection (Wen and Helmberger , 1998b), reduces the amplitudes (relative to a 1-D

model) of SKS-SPdKS phases, and produces strong precursors to ScP and ScS (Wen

and Helmberger , 1998a). The sharp tops of ULVZs inferred seismically (e.g., Rost

et al., 2005) motivated our a priori choice to define a pre-existing sharp bound-

ary separating the chemical component from ambient mantle (e.g., Fig 3.6). If the

iron-rich (Mg,Fe)O-containing component is formed through a diffusive process, for

example by reactions with the core, the interface is not as sharp (e.g., Kellogg and

King , 1993).

Countercirculation is observed in all models, and two cases are shown in Fig. 3.6.

Viscous coupling is energetically favorable because it minimizes viscous shear at the

material interface (e.g., Richter and McKenzie, 1981). Similarly, in a series of labora-

tory tank experiments, Jellinek and Manga (2002) observe a preference for material

to rise along the sloping interface between a low-viscosity chemical layer and ambient

material.

In Fig. 3.6A the ULVZ has sufficient thickness to greatly influence the thermal

structure in the lowermost 90 km, and the two-layer convective regime is clearly

revealed by Profile II in Fig. 3.6C. Isotherms are deflected to lower pressure about

64

5˚10˚ 15˚

2700

2750

2800

2850

REF1 I II III

Dep

th (

km

)

2700

2750

2800

2850

Dep

th (

km

)

CMB-1500 K CMBTemperature

REF1

I

II

III

CMB-1500 K CMB

Temperature

IV

V

VI

REF2

3.0 cm/yr

5˚10˚

REF2 IV V VIA B

C DCMB-1500K CMB

Temperature

Figure 3.6: Steady-state behavior of a thin (Mg,Fe)O-containing layer. (A) Counter-circulation driven by viscous coupling (B = 1.25, dch = 16 km, impermeable domain).The ULVZ component is contained within the area outlined in green and the CMB.(C) Temperature profiles: reference REF1, upwelling I, center II, and downwelling III.(B) Sluggish convection (B = 4, dch = 16 km, permeable domain). (D) Temperatureprofiles (REF2, IV, V, VI) are at the same locations as in (C).

65

the central upwelling, which will determine the stable phase assemblages and melt

generation zones. Our solid-state model does not require partial melt to account for

the dynamic or wavespeed character of ULVZs, but neither is it explicitly excluded. In

this regard, partial melt may explain local variations in ULVZ structure, for example

beneath the Philippine-Kalimantan region (Idehara et al., 2007).

For B & 2, the amplitude of the steady-state perturbation of the chemical layer is

much reduced, approximately 35 km in Fig. 3.6B. The velocity arrows indicate that

this flow is generally sluggish with a recirculation of material accommodated by a low

viscosity channel at the very base of the domain. Conduction is clearly the dominant

heat-transfer mechanism (Fig. 3.6D) and the extreme outcome for this regime is a

ULVZ that is subcritical to convection. In this case the ULVZ would act like a “hot

plate” at the base of the mantle and simply offset the thermal boundary layer to

marginally lower pressure.

Youngs and Houseman (2009) determine that half-width ∝ B0.38 and height ∝

B−0.39 based on calculations in a 3-D Cartesian geometry using an isoviscous fluid.

In our models, however, we have a temperature-dependent viscosity that introduces

a non-linearity which increases the complexity of the convection and questions the

applicability of simple scaling relations that involve B. Given this caveat, we find that

the exponent of B for half-width ranges between 0.76 and 0.37, and for the height

ranges between −0.72 and −0.34.

We now consider the uncertainties in our geodynamic modeling and their impli-

cations. The Rayleigh number affects the morphology of a chemical layer and its

66

topography scales approximately in proportion to Ra−1/3 (Tackley , 1998). We as-

sume a thermal conductivity of around 6.6 W/m-K (e.g., de Koker , 2010) but larger

values (around 28 W/m-K) have been reported (Hofmeister , 2008). The scaling rela-

tion thus predicts that the topography of the chemical layer could be 1.6 times larger

than our model predicts. Similarly, an upper bound for lower mantle viscosity is

two orders of magnitude larger than our reference value (e.g., Ammann et al., 2010),

which by itself could increase relief by a factor of 4.6. Both high thermal conductivity

and lower mantle viscosity could collectively elevate the topography by 7.5 times, but

mid-range estimates predict a more modest increase of a factor of 1.6.

Appropriate activation enthalpies for the deep Earth may induce an order of mag-

nitude viscosity variation (q in Eq. 3.8) greater than 3. For example, assuming a

CMB temperature of 3700 K, a low enthalpy of 500 kJ/mol (Yamazaki and Karato,

2001) results in q ∼ 4, and a higher estimate of 792 kJ/mol (Ammann et al., 2009)

leads to q ∼ 7. When q & 3, instabilities are initially confined to the boundary

layer (Christensen, 1984). Further increasing q reduces the onset time to instability,

decreases the scale of flow, and intensifies the time dependence (Olson et al., 1987).

This eventually leads to a broad-scale well-mixed upwelling with low viscosity (e.g.,

Christensen, 1984; Thompson and Tackley , 1998). Our models do not generate this

type of instability because of the reduced viscosity contrast (q = 3) and the imposed

long-wavelength thermal perturbation. We would expect such a plume to modify the

quantity of residual material at the CMB, although this regime may not be applica-

ble to ULVZs that are only around 2 orders of magnitude weaker than the ambient

67

material (Hier-Majumder and Revenaugh, 2010).

To associate aggregate chemical density anomalies to P-wave velocity (VP ) and

S-wave velocity (VS) of the ULVZs we use a Voigt-Reuss-Hill (VRH) mixing model

(see Watt et al., 1976). We estimate ULVZ properties as a mixture of a silicate

component and a dense oxide, and density anomalies are generated by varying the

fraction of oxide in the solution. In our first mixing model we assume a disequilibrium

assemblage to avoid unnecessary speculation on lowermost mantle mineralogy, and

focus on the combination of properties rather than specific stable coexisting phases.

The composition and properties of the silicate component are not well constrained

in a chemically distinct ULVZ, so we use PREM as the model for its density and

velocity. The dense oxide is assumed to be (Mg0.16Fe0.84)O magnesiowustite (Mw),

as this is the only composition for which extremely low sound velocities have been

measured at appropriate pressures (Wicks et al., 2010). We refer to this model as

“Mw + PREM”. Calculations are made at 121 GPa, the highest pressure reached in

the experimental study, and our model is extrapolated to a high- (4700 K) and low-

temperature (2700 K) estimate of the CMB. The temperature derivatives of velocity

used are ∂VP /∂T = −4.64 × 10−4 (km/s) K−1 and ∂VS/∂T = −3.85 × 10−4 (km/s)

K−1, measured on MgO using a multi-anvil apparatus up to 24 GPa and 1650 K (Kono

et al., 2010). The measured thermal expansion of FeO at 93 GPa, α = 0.54 × 10−5

K−1 (Seagle et al., 2008), is used to estimate the temperature-dependent density of

(Mg0.16Fe0.84)O. Under these assumptions, our VRH mixing model produces a range

of VP and VS for a given chemical density anomaly (Fig. 3.7A, B).

68

-50

-40

-30

-20

-10

0

VP (

% c

han

ge

rela

tiv

e to

PR

EM

)

0 2 4 6 8 10 12

∆ρch/ρ (%) ( = Bα∆T)

TCMB=2700 K

TCMB=4700 K

-50

-40

-30

-20

-10

0

VS (

% c

han

ge

rela

tiv

e to

PR

EM

)

0 2 4 6 8 10 12

∆ρch/ρ (%) ( = Bα∆T)

TCMB=2700 K

TCMB=4700 K

0

50

100

Rel

ief

(km

)

0 1 2 3 4 5 6

B ( = ∆ρch/ρα∆T)

dch = 16 km

dch = 8 km

dch = 4 km

dch = 2 km

Entrainment

No entrainment

Ubiquitous layer

A B

C

Figure 3.7: (A and B). Voigt-Reuss-Hill (VRH) wavespeed determinations at two end-member CMB temperature estimates for the “PREM + Mw” mixing model. Voigt(upper), Reuss (lower), Hill (arithmetic average). See text for model details. (C)Relief of structures for the impermeable cases

69

We also construct a second mixing model to consider the effects of Fe-partitioning

between magnesium silicate perovskite (Pv) and Mw (“Mw + Pv”). Estimates for

the Fe-partitioning between these phases approaching CMB conditions varies between

KPv/MwD ≈ 0.42 for pyrolitic composition (Murakami et al., 2005) and K

Pv/MwD ≈ 0.07

for an Al-free system (e.g., Sakai et al., 2009; Auzende et al., 2008). Trends indicate

that KPv/MwD is likely lower at higher pressures and Fe-content, but it is not possible

to reliably extrapolate from present datasets. This mixing model necessitates a small

KPv/MwD to produce an equilibrium phase assemblage with a bulk density comparable

to PREM and thus density anomalies (equivalently B) that are contained within the

range of this study. Assuming (Mg0.16Fe0.84)O as the oxide phase and with KPv/MwD =

0.07 predicts a coexisting Pv of composition (Mg0.72Fe0.28)SiO3. Such high Fe contents

may be unstable in both Mw (Dubrovinsky et al., 2000) and Pv (Mao et al., 2005),

but other experimental results indicate otherwise (Tateno et al., 2007; Lin et al.,

2003). Possible coexistence of post-perovskite in the presence of Al and Fe adds

further complication (Andrault et al., 2010), so we extrapolate assuming a high CMB

temperature estimate (TCMB = 4700 K) to promote Pv as the stable silicate phase.

Although the presence of Al throughout the lower mantle may alter the partitioning

behavior (e.g., Irifune, 1994) and select thermoelastic properties (e.g., Jackson et al.,

2005), we focus on an Al-free system to simplify the results. The composition and

properties of Pv are determined from a finite strain model (Li and Zhang , 2005) where

effects of Fe are neglected except for a correction to the density. In exploratory models

we perturbed the bulk and shear moduli due to Fe-content (Kiefer et al., 2002) but

70

discovered this had marginal impact. We select an adiabat foot temperature for Pv

that reaches 4700 K at 121 GPa and extrapolate the dense oxide to high temperature

using the same procedure as previously described.

The chemical density anomalies of the mixing models can be directly associated

with the buoyancy numbers used in the geodynamic calculations (Fig. 3.7C). Assum-

ing a high (1500 K) and low (500 K) estimate for the temperature drop at the CMB,

we can therefore predict a relationship between the wavespeed reduction and relief

(thickness) of ULVZs. Our geodynamic models assume ∆T = 1500 K (see Table 3.1),

so we introduce an inconsistency by mapping the data using a reduced ∆T = 500

K, but the Rayleigh number is small (a factor 2-3 difference) and does not alter the

dynamics significantly. Exploring the implications of a high- and low-temperature

drop at the CMB adds to the predictive capabilities of our synthesized model. For

visual clarity we now plot only the Hill bound, and compare to seismic data (Figs. 3.8

and 3.9). For example, in Fig. 3.8B, the “Mw + Pv” model at 4700 K (∆T = 500

K) with relief of 95.7 km produces a VP velocity reduction of ∼ 5% with ∼ 4 vol. %

of Mw. In the same model, ∼ 9% Mw produces a VP reduction of ∼ 9%, resulting in

a relief of 27.5 km.

A negative correlation between ULVZ thickness and wavespeed reduction is ex-

pected given the inherent trade-off in modeling seismic data. This is more evident

with VP (Fig. 3.8A) than VS (Fig. 3.9A). However, this difference may be due to

sampling biases. To discern VP at the base of the mantle the original seismic stud-

ies utilize long-period data which is more sensitive to long wavelength structure. In

71

0

50

100T

hic

knes

s or

reli

ef (

km

)

-30-20-100

VP (% change relative to PREM)

Seismic dataCore reflected

Core scattered

Travel time

0

50

100

Thic

knes

s or

reli

ef (

km

)

-30-20-100

VP (% change relative to PREM)

dch = 16 km

0

50

100

Thic

knes

s or

reli

ef (

km

)

-30-20-100

VP (% change relative to PREM)

dch = 4 km

0

50

100T

hic

knes

s or

reli

ef (

km

)

-30-20-100

VP (% change relative to PREM)

dch = 2 kmTCMB=2700 K, ∆T=500 K

TCMB=4700 K, ∆T=500 K

TCMB=4700 K, ∆T=1500 K

Mw + PREM

Mw + Pv

A B

C D

Figure 3.8: (A) Summary of seismically inferred ULVZ thicknesses and P-wave ve-locity reductions found globally. Following the nomenclature of Thorne and Garnero

(2004): � Precursors to core reflected phases (Mori and Helmberger , 1995; Kohler

et al., 1997; Garnero and Vidale, 1999; Reasoner and Revenaugh, 2000; Havens and

Revenaugh, 2001; Rost and Revenaugh, 2003; Rost et al., 2005, 2006; Hutko et al.,2009; Rost et al., 2010b), △ scattered core phases (Vidale and Hedlin, 1998; Wen and

Helmberger , 1998b; Ni and Helmberger , 2001a; Niu and Wen, 2001), © travel timeand waveform anomalies (Garnero et al., 1993b; Garnero and Helmberger , 1995, 1996;Helmberger et al., 1996, 1998; Wen and Helmberger , 1998a; Helmberger et al., 2000;Simmons and Grand , 2002; Luo et al., 2001; Ni and Helmberger , 2001b; Wen, 2001;Rondenay and Fischer , 2003; Thorne and Garnero, 2004). Filled symbols denote 2-Dstudies. (B, C, and D) Models using the Hill bound, for various dch, temperature atthe CMB (TCMB), and temperature drop (∆T). Solid lines are the “Mw + PREM”model and dotted lines are the “Mw + Pv” model.

72

0

50

100T

hic

kn

ess

or

reli

ef (

km

)

-40-30-20-100

VS (% change relative to PREM)

Seismic dataCore reflected

Travel time

0

50

100

Th

ick

nes

s o

r re

lief

(k

m)

-40-30-20-100

VS (% change relative to PREM)

dch = 16 km

0

50

100

Th

ick

nes

s o

r re

lief

(k

m)

-40-30-20-100

VS (% change relative to PREM)

dch = 4 km

0

50

100T

hic

kn

ess

or

reli

ef (

km

)

-40-30-20-100

VS (% change relative to PREM)

dch = 2 kmTCMB=2700 K, ∆T=500 K

TCMB=4700 K, ∆T=500 K

TCMB=4700 K, ∆T=1500 K

Mw + PREM

Mw + Pv

A B

C D

Figure 3.9: (A) Seismically inferred ULVZ thicknesses and S-wave velocity reductionsfound globally. Following the nomenclature of Thorne and Garnero (2004): � Precur-sors to core reflected phases (Kohler et al., 1997; Garnero and Vidale, 1999; Reasoner

and Revenaugh, 2000; Havens and Revenaugh, 2001; Rost and Revenaugh, 2003; Rost

et al., 2005, 2006; Avants et al., 2006; Hutko et al., 2009; Rost et al., 2010b), © traveltime and waveform anomalies (Garnero and Helmberger , 1995; Helmberger et al.,1998; Wen and Helmberger , 1998a; Helmberger et al., 2000; Simmons and Grand ,2002; Ni and Helmberger , 2001b; Rondenay and Fischer , 2003; Thorne and Garnero,2004; Zhang et al., 2009). Filled symbols denote 2-D studies. (B, C, and D) Modelsusing the Hill bound, for various dch, temperature at the CMB (TCMB), and temper-ature drop (∆T). Solid lines are the “Mw + PREM” model and dotted lines are the“Mw + Pv” model.

73

contrast, shorter-period reflected phases are commonly used to determine VS struc-

ture, and hence thin ULVZs are often detected. For both wavespeeds, a cluster of

datapoints populate a broad range of wavespeed reductions for the thinnest ULVZs,

implying substantial local variations.

The modeled VP and VS can reproduce the seismic observations for a reasonable

range of expected temperatures and temperature drops in the CMB region. 2-D

studies are denoted by filled symbols in Figs. 3.8A and 3.9A. As previously noted,

the seismic data exhibits a broad scatter. Localized variations in ULVZ structure and

material properties, caused by temperature or chemistry, may explain this spread.

However, it is noteworthy that our synthesized model, which combines empirically

determined wavespeeds with geodynamic simulations, is capable of explaining the

current observations.

The PREM mixing model (“Mw + PREM”) intrinsically overestimates the density

and wavespeeds of the silicate component in the cases we explore here, because we do

not explicitly model the silicate at high temperatures (Figs. 3.8 and 3.9). This model

therefore underestimates wavespeed reductions and can be considered a lower bound.

The Fe-partitioning model (“Mw + Pv”) provides insight into the importance of both

Fe-content and temperature in modulating the physical properties and seismic char-

acteristics of ULVZs. Since both Mw and Pv have high Fe contents the compositional

density of the assemblage is high relative to PREM and is therefore likely to form a

flat layer. Higher temperatures, however, reduce total density whilst further reducing

wavespeeds. At TCMB = 4700 K the density of the silicate is sufficiently reduced

74

that a large volume fraction of Mw (also of reduced density) is incorporated into the

assemblage to obtain PREM-like densities. This allows large wavespeed reductions

for relatively small density anomalies.

There are multiple avenues for future work. Limited constraints on the chemistry

and properties of the ULVZ phases under appropriate conditions introduce uncertain-

ties into our VRH mixing model to predict expected VP , VS, and density anomalies.

A better constraint on the temperature and phase relations in D′′, coupled with sound

velocity measurements of these phases at CMB conditions, would help to constrain

the composition. Our geodynamic simulations assume a priori that there is an avail-

ability of FeO-enriched material at the base of the mantle to form ULVZs. It would

therefore be useful to unravel the mechanism for creating an FeO-enriched layer to

constrain its likely volume and iron content. Furthermore, our results are sensitive

to the initial thickness (proxy for volume) of this layer.

3.6 Summary and conclusions

We explore the geodynamic implications of a solid iron-enriched (Mg,Fe)O layer for

the origin of ULVZs. Our numerical simulations produce ULVZs with a sharp and

concave-down seismic top, appropriate horizontal and vertical lengthscales, and an

intrinsic density increase. Models with similar features can explain the scattering

origin of PKP precursors (Wen and Helmberger , 1998b). The morphology and aspect

ratio (relief/half-width) of the structures are strongly dependent on the buoyancy

number B (or equivalently, the chemical density anomaly) and the relief (thickness)

75

is proportional to the initial volume of ULVZ material. Complexities in the thermal

and chemical structure can promote regional variation in ULVZ character.

Wicks et al. (2010) have recently demonstrated that addition of small amounts of

iron-enriched (Mg,Fe)O mixed with silicates may explain the observed reductions in

wavespeeds for ULVZs. We combine our geodynamic results with a Voigt-Reuss-Hill

mixing model and compare with seismic data. For reasonable estimates of the CMB

temperature and temperature drop, our synthesized model satisfies ULVZ wavespeed

reductions and thicknesses inferred seismically, thus lending support to a solid-state

origin for many ULVZs.

76

Chapter 4

Enhanced convection and fast

plumes in the lower mantle

induced by the spin transition in

ferropericlase

Originally published in:

Bower, D. J., M. Gurnis, J. M. Jackson, and W. Sturhahn (2009),Enhanced convection and fast plumes in the lower mantle induced bythe spin transition in ferropericlase, Geophys. Res. Lett., 36, L10306,doi:10.1029/2009GL037706.

4.1 Abstract

Using a numerical model we explore the consequences of the intrinsic density change

(∆ρ/ρ ≈ 2–4%) caused by the Fe2+ spin transition in ferropericlase on the style

and vigor of mantle convection. The effective Clapeyron slope of the transition from

high to low spin is strongly positive in pressure-temperature space and the transition

broadens with high temperature. This introduces a net spin-state driving density

difference for both upwellings and downwellings. In 2-D cylindrical geometry, spin-

buoyancy dominantly enhances the positive thermal buoyancy of plumes. Although

77

the additional buoyancy does not fundamentally alter large-scale dynamics, the Nus-

selt number increases by 5–10%, and vertical velocities increase by 10–40% in the

lower mantle. Advective heat transport is more effective and temperatures in the

core-mantle boundary region are reduced by up to 12%. Our findings are relevant to

the stability of lowermost mantle structures.

4.2 Introduction

A high-spin (four unpaired d electrons) to low-spin (no unpaired d electrons) elec-

tronic transition of divalent iron occurs in ferropericlase (Fp), a major lower mantle

constituent, at around 50 GPa and 300 K (e.g., Badro et al. (2003); Lin and Tsuchiya

(2008); Lin et al. (2007)). The transformation softens the elastic moduli over the tran-

sition pressure range (Lin et al., 2006; Crowhurst et al., 2008). Auzende et al. (2008)

showed that the partition coefficient of iron between Fp and (Fe,Mg)SiO3 perovskite

(Pv) increases, although other experiments have shown little to no effect (Sinmyo

et al., 2008). These results have implications for mantle dynamics and seismic inter-

pretation.

Theoretical (Hofmeister , 1999) and experimental (Badro et al., 2003, 2004) studies

partly motivate geodynamic simulations incorporating increases in radiative thermal

conductivity and viscosity (Matyska and Yuen, 2005, 2006; Naliboff and Kellogg ,

2006). However, contradictory high (Hofmeister , 2008; Keppler et al., 2008) and low

(Goncharov et al., 2008) radiative conductivities need to be reconciled. Arguably, the

most well-defined effect of the spin transition in pyrolite-like Fp is a 2–4% density

78

increase from the high to low spin state at 300 K (Sturhahn et al., 2005; Lin and

Tsuchiya, 2008; Fei et al., 2007), yet the influence on mantle flow has yet to be deter-

mined. The continuous nature of the spin transition along a lower mantle geotherm

(Sturhahn et al., 2005; Tsuchiya et al., 2006) has presumably discouraged such stud-

ies. Downwellings and upwellings may generate substantial temperature anomalies

in the mantle, so that convective flow may be modified by buoyancy forces arising

through the spin-state of the material.

4.3 Numerical models

4.3.1 Spin buoyancy formulation

We modify version 3.0 of the finite element code CitcomS (Zhong et al., 2000; Tan

et al., 2007) to solve the equations for the conservation of mass, momentum, and

energy for incompressible flow. We incorporate a spin-buoyancy body force simil-

iar to a phase function formulation (Richter , 1973; Christensen and Yuen, 1985).

We found that the spin function as determined from a theoretical temperature- and

pressure-dependent spin-state model cannot be accurately represented analytically.

We therefore pre-compute the spin-state model as a function of temperature for each

pressure defined by the radial meshing. Stored as a look-up table, the code accesses

and interpolates the data at each time step to determine the spin-state function. The

additional body force term is equal to the spin-state function multiplied by a spin

Rayleigh number. Since latent heat is a non-Boussinesq effect (Christensen and Yuen,

79

1985), the entropy changes associated with the spin transition are not included in the

energy equation. In previous studies, latent heat has been found to be of secondary

importance in mantle phase transitions (Olson and Yuen, 1982).

We select the (Mg83Fe17)O spin-state model (Sturhahn et al., 2005), except that

the model is translated by -10 GPa in accordance with recent experimental results

showing that the transition at 300 K occurs at about 50 GPa (see Lin and Tsuchiya

(2008) for a review). We non-dimensionalize by a surface temperature, T0 = 300

K, temperature drop, ∆T = 2700 K, and a pressure scale of 40 MPa/km. For this

particular model, the high-low spin density contrast is reported to be 2.3%, consistent

with high-pressure x-ray diffraction studies (Lin and Tsuchiya, 2008).

4.3.2 Model setup

We develop a suite of models with the Boussinesq approximation within a 2-D section

(1 radian). The mesh size is 257 x 129 nodes with refinement in the radial direction

within the boundary layers. Isothermal and free-slip boundary conditions are im-

posed at the top and bottom boundaries and the two sidewalls have a zero heat flux

boundary condition.

Viscosity is computed by a temperature-dependent linearized Arrhenius law, η(T ) =

η0exp(A(0.5 − T )), where η0 = 1 for the upper mantle, 10 for the transition zone,

and 30 for the lithosphere and lower mantle. The reference value is 1021 Pa·s at

T = 0.5. The activation energy, A, and thermal and spin Rayleigh number, Ra are

free parameters (Table 4.1). Ra spans a range to contrast vigourous upper mantle

80

convection with sluggish lower mantle convection. To ensure mobile-lid convection,

we use low activation energies so that the viscosity contrast is less than four orders of

magnitude. The phase changes within the mantle are not included, so that the effect

of the Fe2+ spin transition is isolated. Internal heat sources are not considered.

4.3.3 Procedure

After integrating from a conductive temperature profile for 100,000 time steps (di-

mensionally several Ga) the system has a reached statistical steady state, as evident

through small oscillations of the top and bottom Nusselt numbers (Nu) and the lat-

erally averaged temperature profile. Two models are then initialized from the final

state: The first with the spin transition, and the second without. Both are integrated

for a further 100,000 time steps. In addition to observing the pattern of convection,

we apply three measures to determine the influence of the spin transition. At steady

state, we compare time-averaged top and bottom Nu’s and depth profiles for the hor-

izontally averaged temperature (reference geotherm) and RMS vertical velocity. We

only report the top Nu because for most cases the Nu’s differ by only a fraction of a

percent (Table 4.1).

4.4 Results

The spin-state model reveals a strongly positive effective Clapeyron slope (Fig. 4.1d).

Relative to the reference geotherm, this generates buoyancy by transforming cold

(warm) material to the more- (less-) dense phase at a lower (higher) pressure. The

81

(a)

0

500

1000

1500

2000

2500

0.0 0.5 1.0

Temperature

(b)

0

500

1000

1500

2000

2500

De

pth

(km

)

0.0 0.5 1.0

Temperature

(c)

0

500

1000

1500

2000

2500

0 2 4

Average unpaired electrons

(d)

0

500

1000

1500

2000

2500

De

pth

(km

)

01234

Average unpaired electrons

(Sns, Pns)

(e)

0

500

1000

1500

2000

2500

−1 0 1δρ/α∆T

(f)

Figure 4.1: Snapshot from Case 13 at quasi-steady state. (a) Non-dimensional tem-perature. The purple and green lines delineate the location of representative warmand cold geotherms respectively, referred to in subsequent panels. (b) Unpaired elec-trons (spin-state) for representative warm (purple) and cold (green) geotherms. Reddot is (Sns,Pns) for the spin-state model (see text). Black dashed line is the reference(horizontally averaged) spin-state. (c) Unpaired electrons with geotherm locations.(d) Geotherms with Sturhahn et al. (2005) spin-state model. Black dashed line is thereference geotherm. (e) Spin density anomaly, scaled by 1/α∆T , relative to the hor-izontally averaged profile. Contour interval is 0.1. (f) Total density anomaly, scaledby 1/α∆T , relative to the horizontally averaged profile. Contour interval is 0.2.

82

0

500

1000

1500

2000

2500

Depth

(km

)

0 10 20 30 40

δ RMS(Vvertical) (%)

C3C4C5C11

(a)

0

500

1000

1500

2000

2500D

epth

(km

)

−10 0 10 20 30

δ Temperature (%)

C3C4C5C11

(b)

Figure 4.2: Fractional change (horizontally averaged) caused by the spin transition(%) for representative cases at quasi-steady state. (a) RMS vertical velocity. (b)Temperature

temperature broadening envelope causes cold (warm) material to transform within a

tight (broad) pressure range. This introduces a neutral spin-buoyancy pressure (Pns)

at which the spin-state (Sns), biased toward high-spin, is independent of temperature

(Fig. 4.1b). This arises through the approximately temperature-independent spin

contour at Pns, and explains the common intersection point for the representative

geotherms.

83

Tab

le4.

1:In

put

and

outp

ut

char

acte

rist

ics

ofth

em

odel

s.R

ais

the

Ray

leig

hnum

ber

,A

isth

eac

tiva

tion

ener

gy,

and

regi

me

indic

ates

the

style

ofco

nve

ctio

n.

Nu

isth

eN

uss

elt

num

ber

and

Vz

isth

eve

rtic

alve

loci

tyat

2500

km

dep

th.

“n”

and

“s”

subsc

ripts

den

ote

model

sw

ithou

tan

dw

ith

the

spin

tran

sition

,re

spec

tive

ly.

Ast

andar

ddev

iati

onis

give

nfo

rth

eti

me-

dep

enden

tca

ses.

∆N

uan

d∆

Vz

are

the

chan

gein

the

Nuss

elt

num

ber

and

vert

ical

velo

city

due

toth

esp

intr

ansi

tion

.C

ase

Input

Outp

ut

Ra

AR

egim

eN

un

Nu

s∆

Nu(%

)V

z nV

z s∆

Vz

(%)

15×

106

0Ste

ady

11.4

012

.47

9.4

338.

041

9.3

24.1

25×

106

4Ste

ady

9.52

10.4

39.

525

6.3

334.

830

.63

106

6Ste

ady

8.79

9.64

9.7

240.

133

4.7

39.4

41×

107

0Ste

ady

11.5

112

.65

9.9

404.

650

1.7

24.0

51×

107

4Ste

ady

11.5

612

.66

9.5

384.

249

8.3

29.7

61×

107

6Ste

ady

10.5

411

.57

9.9

358.

449

6.3

38.5

75×

107

0Ste

ady

19.4

721

.15

8.6

1178

.514

36.2

21.9

85×

107

4T

ime-

dep

enden

t18

.11±

0.11

19.1

0±0.

225.

595

9.2±

15.2

1195

.7±

59.3

24.7

95×

107

6T

ime-

dep

enden

t13

.10±

0.61

14.1

3±0.

627.

956

9.4±

116.

973

7.7±

204.

929

.610

108

0T

ime-

dep

enden

t24

.39±

0.03

26.1

3±0.

437.

117

02.5±

2.4

2091

.6±

88.4

22.9

111×

108

4T

ime-

dep

enden

t21

.37±

0.49

22.6

7±0.

416.

113

73.1±

84.0

1707

.4±

115.

324

.012

108

6T

ime-

dep

enden

t16

.56±

0.64

17.3

7±1.

264.

986

4.4±

200.

410

61.2±

223.

122

.813

108

4T

ime-

dep

enden

t30

.55±

2.35

31.8

0±2.

334.

129

81.8±

639.

932

76.3±

683.

89.

9

84

The spin transition increases vertical velocities throughout the mantle (Fig. 4.2a)

with 10-40% increases in the lowermost mantle, tapering to near zero at the surface.

Temperatures in the interior of the mantle are raised by up to 12%, except for the

region above the core-mantle boundary (CMB) where they are reduced by an average

of 5% (Fig. 4.2b). For both of these profiles, the percentage increase is inversely

proportional to Ra and scales with A. The Nusselt number increases between 4 and

10% (Table 4.1) and scales inversely with Ra.

High temperatures within the lower thermal boundary layer (Figs. 4.1a and 4.1d)

cause instabilities to develop with a bias toward high spin-state (Fig. 4.1c). At depth,

these upwellings have both positive thermal and spin buoyancy that generates higher

advective velocities (Fig. 4.2a). This increases the rate of heat removal, consistent

with the reduced temperatures above the CMB in our models (Fig. 4.2b). Driving

spin-state density differences in upwellings are distributed over a broad pressure range

(Fig. 4.1e). As material passes through Pns, the spin-buoyancy changes from working

with thermal buoyancy to mildly opposing it (Fig. 4.1b). Thermal forcing continues

to drive upward advection (Fig. 4.1f), albeit at a reduced velocity. Downwellings

are less affected by the spin transition as the net change in buoyancy about Pns is

negligible because of smaller temperature differences between cold and ambient ma-

terial than for warm, particularly at high pressure (Fig. 4.1d). This is controlled, in

part, by the cylindrical geometry, rheological law, and pure basal heating. Driving

spin-state density differences within downwellings are constrained within a compara-

tively tight pressure range (Fig. 4.1e). Positive spin-state buoyancy at pressures less

85

than Pns slightly retards downward advection, but at greater pressures spin-buoyancy

mildly enhances downward motion. Therefore, both upwellings and downwellings are

impeded by spin-buoyancy at pressures less than Pns and are enhanced at pressures

greater than Pns. The asymmetry (Sns < 2) of the spin-state model ensures that a

net force exists in both cases.

4.5 Discussion and conclusions

The dominant effect of buoyancy caused by the spin transition is comparable to a

strongly exothermic phase change, similar to a discrete phase change (Christensen

and Yuen, 1985). However, the nature of the Fe2+ spin transition generates buoyancy

over a broader pressure range for upwellings than for downwellings. Spin-forcing de-

pends strongly on temperature contrasts, with our models predicting increased plume

velocities and heat transfer, and marginally reduced temperatures above the CMB.

The temperature-broadening of the transition precludes significant perturbation to

the bulk Earth 1-D velocity profile (Masters , 2008). Seismic detection will require

a focus on cold slabs where the transition occurs abruptly with the potential for a

seismic discontinuity. A detailed mapping of localized structures to observed seismic

velocities requires more accurate knowledge of the high P-T wave speeds in candidate

phase assemblages.

The spin transition, in addition to the Pv-pPv phase change, is a destabilizing

mechanism in the lowermost mantle that will further work against the stability of

high-density (McNamara and Zhong , 2005) or high-bulk modulus (Tan and Gurnis ,

86

2005) structures. Furthermore, it provides additional buoyancy to small-scale hot

plumes, such as those that possibly emanate from the edges of large, low-velocity

structures (Sun et al., 2009a). Transient systems with non-Newtonian rheology and 3-

D geometry may behave differently. Additionally, iron concentration in Fp affects the

transition pressure (e.g., Fei et al., 2007), and iron-enriched upwellings and depleted

downwellings may have different spin-state models.

87

Chapter 5

Lower mantle structure from

paleogeographically constrained

dynamic Earth models

To be submitted as:

Bower, D. J., M. Gurnis, and M. Seton (2012), Lower mantle structure frompaleogeographically constrained dynamic Earth models, Geochem. Geophy.Geosy.

5.1 Abstract

Seismic tomography reveals two large, low-shear velocity provinces (LLSVPs) beneath

Africa and the Pacific Ocean. These structures may have existed for several 100 Myrs

and are likely compositionally distinct based on observed seismic, geodynamic, and

mineral physics characteristics. We investigate the dynamics of the LLSVPs through

the use of evolutionary models of thermochemical structures from 250 Ma to present

day. We use a 3-D spherical convection model in which the anomalous structures

have a high bulk modulus, consistent with seismic interpretation. A new progressive

assimilation method incorporates constraints from paleogeography using a refined

plate history model (with 1 Myr time spacing) to guide the thermal structure of

88

the lithosphere and steer the therml evolution of slabs in the uppermost mantle.

The thermochemical structures deform and migrate along the core-mantle boundary

(CMB), either by coupling to plate motions or in response to slab stresses. The

models produce a ridge-like anomaly beneath Africa and a rounded pile beneath the

Pacific Ocean. However, slabs from the Tethys Ocean push the African structure

further to the southwest than inferred from tomography. Dense and viscous slabs can

severely compromise the stability of high bulk modulus structures at the CMB.

5.2 Introduction

Seismic tomography (Fig. 5.1a,b) reveals two large, low-shear velocity provinces

(LLSVPs) at the base of the mantle beneath Africa and the Pacific Ocean with ap-

proximately a degree-two pattern. These structures contain 1.5–2.4 vol. % and ∼ 2

mass % of the mantle and occupy almost 20% surface area of the core-mantle bound-

ary (CMB) (e.g., Hernlund and Houser , 2008; Burke et al., 2008). A thermochemical

origin is necessary to explain anti-correlated shear wave and bulk sound velocity

anomalies (Su and Dziewonski , 1997; Masters et al., 2000), putative anti-correlated

shear wave and density anomalies (Ishii and Tromp, 1999, 2004), multipathing for

waves sampling its steep edges (Ni et al., 2002), and geological inferences of stability

over 200–300 Myr (Burke and Torsvik , 2004). Waveform modeling identifies the finer-

scale structure and refines the geographical extent of the LLSVPs. This technique

is particularly useful to address ambiguity in tomography models by resolving the

vertical extent of the structures and the wavespeed reduction and thickness of the

89

basal layer.

Ritsema et al. (1998) present compelling evidence for a large mid-mantle structure

beneath Africa by satisfying travel-time data for S, ScS, and SKS, along a corridor

from the Drake passage to the Hindu Kush. The African LLSVP rises 1500 km

above the CMB with an S wavespeed reduction of 3%. This is also supported by

the first arrival cross over of SKS to S from South American events to world-wide

standard seismographic network (WWSSN) stations in Africa (Ni et al., 1999). These

early studies identify strong shear velocity gradients at the edges and top of the

structure. Ni et al. (2002) attribute SKS waveform complexity to in-plane (2-D)

multipathing and use the travel-time delays to determine a boundary width of less

than 50 km. They further suggest the eastern edge of the bulk of the anomaly is

tilted toward the northeast, in agreement with some tomography models (Ritsema

et al., 1999) (Fig. 5.1c). Alternatively, Wang and Wen (2007a) use more data from

events northeast of the anomaly to argue that this flank tilts to the center and the

basal layer extends farther northeast.

The thickness and velocity reduction of the basal layer at the CMB beneath

the African structure remains contentious. Beneath the eastern part of the South

Atlantic, Wen et al. (2001) propose a 300-km-thick anomaly with much lower S

wavespeeds linearly decreasing from -2% at the top to about -10% at the base (also see

Wen, 2002). P and S core reflected phases support this interpretation (Simmons and

Grand , 2002). Wen (2001) extend this feature beneath the Indian Ocean by mod-

eling several corridors of data and ascribe travel-time delays to variations in layer

90

-60˚ -60˚

0˚ 0˚

60˚ 60˚

Bulk soundf) SB10L18

-1.0 -0.5 0.0 0.5 1.0

δvc (%)

-60˚ -60˚

0˚ 0˚

60˚ 60˚

S-wavee) SB10L18

-3 -2 -1 0 1 2 3

δvs (%)

0

1000

2000

S-waved) Pacific LLSVP (S40RTS)

-1.5 0.0 1.5

δvs (%)

0

1000

2000

S-wavec) African LLSVP (S40RTS)

-1.5 0.0 1.5

δvs (%)

-60˚ -60˚

0˚ 0˚

60˚ 60˚

S-waveb) Contour

-60˚ -60˚

0˚ 0˚

60˚ 60˚

S-wavea) S40RTS

-3 -2 -1 0 1 2 3

δvs (%)

A B C D

SB10L18 S40RTS TXBW

A

B

C

D

Figure 5.1: Seismic tomography data for the LLSVPs. (a, e) Shear velocity tomog-raphy models at 2800 km depth. (a) S40RTS (Ritsema et al., 2011), (e) SB10L18(Masters et al., 2000). (b) -0.6% shear velocity contours from several S-wave tomogra-phy models (SB10L18, S40RTS, TXBW (Grand , 2002)) at 2800 km depth show thatthey are consistent. (c, d) Cross section through the African and Pacific LLSVPs,respectively. The color scale is saturated to highlight mid-mantle structure. Locationof cross sections are marked on (a). (f) Bulk sound speed from SB10L18 (Masters

et al., 2000) at 2800 km depth. Note approximate anticorrelation with shear velocityin (e).

91

thickness. However, others favor a moderate basal layer with -3% S wavespeed (e.g.,

Ni and Helmberger , 2003b,c). This later model attributes some of the travel-time

delays to the mid-mantle structure, particularly for SKS paths, and thus the basal

wavespeed reduction is less. The geographical footprint on the CMB is the same

regardless of the vertical extent of the anomaly (e.g., Wang and Wen, 2004).

Ni and Helmberger (2003a) model the 3-D geometry of the African LLSVP as

a ridge-like structure approximately 1200 km high and 1000 km wide that extends

7000 km along the CMB from Africa to the Indian Ocean. By contrast, the more

extreme basal layer model is compatible with a limited and localized mid-mantle

extension (e.g., Wen, 2006). Definitive confirmation of either model is limited by

sparse data coverage for azimuths other than the Drake Passage to Hindu Kush

corridor (Helmberger and Ni , 2005). 3-D multipathing along strike of the African

structure (Ni et al., 2005; To et al., 2005) or extreme wavespeed reductions in the

basal layer can both explain delayed S-wave postcursors. New seismic tools are being

developed to address such ambiguities by helping to distinguish between in-plane (2-

D) multipathing caused by horizontal structure and out-of-plane (3-D) multipathing

due to vertical structure (Sun et al., 2009b).

The African structure also exhibits small-scale features. Ultralow-velocity zones

(ULVZs) are detected at the edges of the LLSVP, with one extending at least 800 km

along the eastern boundary beneath central Africa (Helmberger et al., 2000; Ni and

Helmberger , 2001a). Another is located between Madagscar and Africa (Wen, 2000)

and a third beneath Tristan (Ni and Helmberger , 2001b). Shear wave anisotropy

92

has been interpreted as revealing complex flow occuring at the edges (Wang and

Wen, 2007b) suggesting strong interactions between the LLSVP and ambient mantle.

Recently, Sun et al. (2010) provide waveform evidence for a small plume with a

diameter less than 150 km emanating from the top of the structure beneath southern

Africa.

The Pacific LLSVP is less well imaged than its African counterpart because of

source receiver geometry and its location beneath the vast Pacific Ocean. He and

Wen (2009) construct a comprehensive model along a great arc from East Eurasia

to South America using S, Sd, ScS, SKS, and SKKS phase. Their model divides the

LLSVP into a western and eastern province separated by a ∼ 700 km gap that occurs

beneath the Fiji Islands. The western province rises 740 km above the CMB and

is 1050 km wide at the base, with edges conjectured to be steeper than the African

structure. The eastern section is 340–650 km high and 1800 km wide. This overall

geometry is also evident in tomography (e.g., Fig. 5.1d). Each province resembles a

trapezoid with a lateral dimension that increases with depth with an S wavespeed

reduction of 3% and 5% in the interior and basal portions, respectively (He and Wen,

2009). Another cross section from Fiji-Tonga to California uses multibounce S and

ScS phases to overcome the lack of stations in the ocean basin (Liu et al., 2011).

These authors report an overall average height of 600 km with an average anomalous

S velocity of -2% and make note of its geometric complexity in comparison to the

apparently more simple African LLSVP.

Sharp edges are identified at the margins of the Pacific structure to the south

93

(To et al., 2005), east (e.g., Liu et al., 2011), and west (Takeuchi et al., 2008). The

northeast boundary abuts a ULVZ or a slow basal layer which is overlain by a high-

velocity region (∼ 120 km thickness) that extends further to the northeast (He et al.,

2006; He and Wen, 2009). Numerous ULVZs are detected at the southwest margin

(see Thorne and Garnero, 2004) and a few are situated beneath the LLSVP (e.g., Liu

et al., 2011).

Geodynamic calculations have attempted to reproduce the long-wavelength mor-

phology of the LLSVPs; a linear ridge-like feature beneath Africa and a rounded pile

beneath the Pacific Ocean. Early 3-D Cartesian thermochemical convection stud-

ies with temperature-dependent viscosity only produce ubiquitous ridge-like features

(Tackley , 1998, 2002). Spherical geometry alone is unable to produce rounded piles

without assigning a higher intrinsic viscosity to the LLSVPs, and ridges and piles do

not coexist (McNamara and Zhong , 2004).

Plate motion history can control the location and morphology of the LLSVPs

as shown in models (McNamara and Zhong , 2005) that use a global tectonic recon-

struction since 119 Ma (Lithgow-Bertelloni and Richards , 1998). Zhang et al. (2010)

recently extended this model by constructing a few, conjectural plate stages back

to 450 Ma to further investigate LLSVP mobility and stability using incompressible

models with a high-density basal layer. They argue that prior to Pangea forma-

tion the African mantle was dominated by downwellings from convergence between

Laurussia and Gondwana. The downwellings pushed the chemically distinct material

south of Gondwana and into the Pacific hemisphere, forming a single pile. Subsequent

94

circum-Pangea subduction, particularly on the southeast side of the supercontinent,

split the chemical pile into two, forming the African LLSVP. This suggests the Pacific

structure has existed since the Early Paleozoic whereas the bulk of the African struc-

ture formed at 230 Ma, about 100 Myr after the assembly of Pangea. Zhong et al.

(2007) show that this implies an interaction of degree-one mantle convection and the

supercontinent cycle.

The reconstructed eruption sites of large igneous provinces (LIPs) (since 300 Ma)

(Burke and Torsvik , 2004; Burke et al., 2008), major hotspots (Burke et al., 2008),

and kimberlites (since 320 Ma) (Torsvik et al., 2010) correlate with the edges of

the African and Pacific LLSVPs. Burke et al. (2008) therefore propose that the

boundaries of the LLSVPs at the CMB are ‘Plume Generation Zones’ (PGZs). This

hypothesis suggests that the African and Pacific structures have been independent

and stable since before 300 Ma and may be insensitive to plate motions, contrary to

the models of Zhang et al. (2010). Furthermore, the existence of older LIPs (since

2.5 Ga) suggest LLSVPs earlier in Earth history, although they are not necessarily

derived from the same structures that exist today (Burke et al., 2008).

A chemically distinct component with a high bulk modulus (high-K) generates

structures that satisfy geodynamic and seismic constraints on the LLSVPs (Tan and

Gurnis , 2005, 2007; Sun et al., 2007). Recent calculations in a spherical geometry

reveal the propensity for stronger plumes to develop at the edges of such domes

compared to their tops, providing a potential dynamic model for the PGZs (Tan et al.,

2011). Since high-K structures rely on a balance between thermal and compositional

95

buoyancy the net density anomaly (relative to ambient mantle) is often small. While

this facilitates domes with high relief and sharp, steep boundaries, it may render

the structures passive to the circulation induced by plate motions. Subduction zone

geometry influences the location of the domes and therefore it may be problematic to

maintain the spatial stability of high-K structures for several hundred million years

(Tan et al., 2011).

In this study we investigate the stability and morphology of LLSVPs with high-K

in a mantle constrained by the tectonic evolution of the lithosphere from 250 Ma

to the present. Our models incorporate several advances: (1) a new global tectonic

reconstruction (Seton et al., 2012) with continuously closing plate polygons (Gurnis

et al., 2012a) that has much finer spatial and temporal resolution while being con-

sistent with the details of global geology; (2) constraints on the thermal evolution of

the lithosphere through the assimilation of reconstructed seafloor ages; (3) steering

the evolution of slabs in the uppermost mantle using the new tectonic reconstruction

and a thermal slab model through progressive data assimilation.

5.3 Numerical models

5.3.1 Governing equations

We apply the extended Boussinesq and Boussinesq approximation (hereafter EX and

BO, respectively) (Ita and King , 1994) to model thermochemical convection using fi-

nite element models. The finite element problem is solved with CitcomS (Zhong et al.,

96

2000, 2008) which is modified to incorporate a depth-dependent chemical density

anomaly (e.g., Tan and Gurnis , 2007) to simulate the effect of a high bulk modulus

material. The equation for the conservation of mass is:

∇ · u = 0 (5.1)

where u is velocity. The non-dimensional momentum equation is:

−∇P + ∇ · τ = (Γ−1∆ρchC − αT )Ragr (5.2)

where P is dynamic pressure, τ deviatoric stress tensor, α coefficient of thermal

expansion, T temperature, ∆ρch chemical density, C concentration of composition-

ally distinct material, Ra thermal Rayleigh number, g gravity, and r radial unit

vector. Overbars denote radially dependent input parameters and “0” subscripts de-

note dimensional reference values (Table 5.1). Maximum thermal density anomaly

Γ = ρ0α0∆T , where ρ0 is density and ∆T is the temperature drop across the mantle.

The Gruneisen parameter (γ) is used a priori to construct the depth-dependent

chemical density (∆ρch) by integrating the self-compression equations for two

chemistries with different bulk moduli and zero-pressure density (see Tan and Gurnis ,

2007, for details). We report the chemical density anomaly at the CMB (δρch) and the

bulk modulus anomaly (δ K) (Table 5.2). The usual definition of the buoyancy num-

ber, B is recovered for depth-independent chemical density anomaly, B = Γ−1∆ρch.

97

Table 5.1: Generic model parametersParameter Symbol Value Units Non-dim Value

Rayleigh number (Eq. 5.3) Ra - - 1.83 × 108

Dissipation number Di - - 1.74Density ρ0 3930 kg m−3 1

Thermal expansion coefficient α0 3 × 10−5 K−1 1Earth radius R0 6371 km 1

Gravity g0 10 m s−2 1Thermal diffusivity κ0 10−6 m2 s−1 1

Heat capacity cp0 1100 J kg−1 K−1 1Temperature drop ∆T 3000 K 1Reference viscosity η0 5 × 1021 Pa s 1

Activation energy (Eq 5.7) E 172 kJ mol−1 6.908Surface temperature TS 300 K 0.1

Heating rate H 3.2×10−8 W m−3 100Gruneisen parameter γ - - 2.3

The Rayleigh number is defined as:

Ra =ρ0α0∆TR0

3g0

η0κ0

(5.3)

where R0 is Earth radius, η0 viscosity, and κ0 thermal diffusivity (Table 5.1). This

definition uses the Earth radius rather than mantle thickness and is thus about an

order of magnitude larger than the normal definition.

The energy equation (non-dimensional) is:

cp∂T

∂t= −cpu · ∇T + ∇ · (cpκ∇T ) − Di(T + TS)αgur +

Di

Raτ : ǫ + H (5.4)

where cp is heat capacity, Di = α0g0R0/cp0 is dissipation number, TS is surface

temperature, ǫ is strain rate tensor, and H is internal heating rate (Table 5.1).

The usual definition for the Boussinesq approximation ignores depth-dependent

98

material properties and heating terms involving Di. However, since high-K structures

necessitate pressure-dependent parameters, our BO models only neglect the additional

heating terms (Di = 0).

The equation for chemical advection is:

∂C

∂t+ (u · ∇)C = 0. (5.5)

We advect tracers representing the chemical components using a predictor-corrector

scheme (McNamara and Zhong , 2004) and determine composition using the ratio

method (Tackley and King , 2003).

5.3.2 Model setup

The full sphere is constructed of 12 caps, each with 128×128×64 elements, giving

a total of ∼ 12.6 million elements. Radial mesh refinement provides the highest

resolution of 18 km in the boundary layers and a minimum resolution 90 km in the

mid-mantle.

High-K domes can form for a range of thermal expansion profiles that decrease

with pressure from the surface to the CMB (see Tan and Gurnis (2007), Fig. 3).

Conversely, the behaviour of thermal slabs is extremely sensitive to this reduction.

Too large of a decrease will invariably hinder and potentially stall downgoing slabs,

particularly when coupled with a stiff lower mantle (Hansen et al., 1991, 1993). To

facilitate interaction between the domes and slabs we therefore opt for a simple pa-

rameterization to decrease the thermal expansion coefficient with pressure by a factor

99

mα across the mantle:

α =1

2

(

ro − r

ro − ri

+ mαr − ri

ro − ri

)

(5.6)

where ro = 1 is the (non-dimensional) outer radius of the sphere and ri = 0.55 is the

inner radius. Varying mα allows us to compare slab descent rates in the lower mantle

with estimates using geological tomography correlations (van der Meer et al., 2010).

Note that our definition of mα is different from that used by Tan and Gurnis (2007).

Our formulation sets the thermal expansion coefficient at the CMB to eliminate a

trade-off with the magnitude of the chemical density profile. The thermal expansion at

the surface is a factor of mα larger. Therefore, advective heat transport is enhanced for

models with a larger mα because the effective Rayleigh number is greater, particularly

in the uppermost mantle.

Our CMB thermal expansion coefficient is dimensionally 1.5 × 10−5 K−1, which

compares favorably with MgSiO3 perovskite at 88 GPa and 3500 K (Oganov et al.,

2001; Marton and Cohen, 2002) and is slightly larger than bulk mantle estimates of

approximately 1 × 10−5 K−1 (Stacey , 1977; Hama and Suito, 2001). We define the

reference thermal expansion coefficient α0 = 3 × 10−5 K−1 (Stacey , 1977), which is

also comparable with perovskite at ambient conditions (Katsura et al., 2009).

We adopt a purely diffusion creep constitutive relation which is likely to be ap-

propriate for the lower mantle (Karato and Li , 1992). Dislocation creep and yielding

are critical for the motion of plates and slabs (Billen and Hirth, 2007; Stadler et al.,

2010). However, because of assimilated plate kinematics and slab structure in the

upper mantle (see next section) we effectively remove the need to include these com-

100

plexities. Viscosity (non-dimensional) is composition dependent:

η(T, r) = η0(r)(1 + ηCC) exp[E(0.5 − T )] (5.7)

where η0(r) is a radially dependent prefactor, ηC is intrinsic compositional viscosity

prefactor, and E is non-dimensional activation energy. η0(r) = 1 for the lithosphere

(0–100 km depth) and η0(r) = 1/30 for the upper mantle (100–670 km depth). For

the lower mantle η0(r) increases linearly from 2.0 at 670 km depth to 6.8 at the CMB

(Zhang et al., 2010). This pressure-induced viscosity increase offsets the decrease

caused by the adiabatic temperature gradient. E = 6.908 generates 103 viscosity

variation due to temperature (Table 5.2).

We apply a free slip and isothermal (T = 1) boundary condition at the CMB

and a kinematic and isothermal (T = 0) boundary condition at the top surface.

The upper thermal boundary layer is characterized by large velocity gradients and

high viscosity due to the temperature-dependent rheology and the imposed 30× step

increase from the upper mantle. In the EX framework viscous dissipation produces

intense localized heating at plate boundaries. This produces large gradients in strain

rate and viscosity which can cause numerical difficulties. Furthermore, a range of

deformation mechanisms operate in the lithosphere that cannot be simply modeled

by diffusion creep. We therefore set the dissipation number, Di to zero for depths

less than 325 km.

101

-60˚ -60˚

0˚ 0˚

60˚ 60˚

f) 0 Ma

-60˚ -60˚

0˚ 0˚

60˚ 60˚

e) 50 Ma

-60˚ -60˚

0˚ 0˚

60˚ 60˚

d) 100 Ma

-60˚ -60˚

0˚ 0˚

60˚ 60˚

c) 150 Ma

-60˚ -60˚

0˚ 0˚

60˚ 60˚

b) 200 Ma

-60˚ -60˚

0˚ 0˚

60˚ 60˚

a) 250 Ma

0 50 100 150 200 250

Seafloor Age (Ma)5 cm/yr

Figure 5.2: Snapshots of the plate tectonic reconstruction (Seton et al., 2012) (a) 250Ma, (b) 200 Ma, (c) 150 Ma, (d) 100 Ma, (e) 50 Ma, (f) present day. Ridges andtransform faults are represented by red lines and subduction zones are represented byblack lines with sawteeth indicating polarity. Non-oceanic regions are dark grey andreconstructed continents with present-day shorelines are shown in light grey (exceptblack for the present day).

102

5.3.3 Data assimilation

We use progressive assimilation of a thermal and kinematic model of surface plate

evolution with continuously closing plates at 1 Myr intervals (Fig. 5.2) (Seton et al.,

2012). The plate motion model is based on a merged moving Indian/Atlantic hotspot

reference frame (O’Neill et al., 2005) for the past 100 Myrs and a true polar wander-

corrected reference frame (Steinberger and Torsvik , 2008) for older times. The Pacific

is anchored to fixed Pacific hotspots prior to 83.5 Ma based on a merged Wessel et al.

(2006) and Wessel and Kroenke (2008) reference frame. The proto-Pacific/Panthalassa

evolved from an Izanagi-Farallon-Phoenix triple junction. Importantly, the plate

model incorporates the break-up of the Ontong Java-Manihiki-Hikurangi plateaus

between 120-86 Ma. The Tethys Ocean is reconstructed largely based on a combina-

tion of Stampfli and Borel (2002) and Heine et al. (2004). GPlates (Gurnis et al.,

2012a) exports plate velocities from the digitized plate boundary dataset, providing

the kinematic boundary condition on the top surface with linear interpolation between

the plate model ages. Therefore, in the convection calculations we do not remove net

angular momentum or rigid body rotation.

We create a thermal model for the lithosphere using reconstructed seafloor ages

and a half-space cooling model (Fig. 5.3). A thermal age of 200 Ma is assigned to

non-oceanic regions. At each time step in the computation, for depths ≤ 60 km,

the code blends the lithosphere thermal model with the temperature field from the

previous time step (see, Matthews et al., 2011, for details). This approach suppresses

convective instabilities away from convergent plate margins and dictates the global

103

0˚5˚ 10˚ 15˚

20˚

0

500

1000

i)h)

0.0 0.5 1.0

Temperature

10˚

20˚

30˚

40˚

50˚g)

0 50 100 150

Age (Ma)

0˚5˚ 10˚ 15˚

20˚

0

500

1000

f)e)

10˚

20˚

30˚

40˚

50˚d)

0˚5˚ 10˚ 15˚

20˚

0

500

1000

c)

60˚ 70˚ 80˚ 90˚ 100˚ 110˚

b)

60˚ 70˚ 80˚ 90˚ 100˚ 110˚

10˚

20˚

30˚

40˚

50˚a) 250 Ma 250 Ma 250 Ma

240 Ma 240 Ma 240 Ma

230 Ma 230 Ma 230 Ma

A

B

C

D

E

F

A B

C D

E F

5 cm/yr

Figure 5.3: Progressive data assimilation example for the convergence of the Paleo-Tethys Ocean and Laurussia (Model EX1). Plate history and age of oceanic litho-sphere model (a) 250 Ma, (d) 240 Ma, (g) 230 Ma. Temperature field at 110 kmdepth (b) 250 Ma, (e) 240 Ma, (h) 230 Ma. Cross section of slab (c) profile A–B, 250Ma, (f) profile C–D, 240 Ma, (i) profile E–F, 230 Ma. Ridges and transform faultsare represented by red lines and subduction zones are represented by black lines withsawteeth indicating polarity. Non-oceanic regions are dark grey.

104

surface heat flux.

To construct a thermal slab model we use the paleolocation and age of the oceanic

lithosphere at convergent plate margins. We then select a slab dip angle (45◦ for

simplicity) and apply a half-space cooling model either side of the slab center line

to conserve buoyancy. This thermal structure is assimilated at each time step using

a blending stencil. The method ensures that slab buoyancy in the upper mantle

is consistent with surface plate evolution and allows our simulations to capture the

essential aspects of subduction such as asymmetric geometry and slab roll-back (see,

Gurnis et al., 2012b, for details).

5.3.4 Parameter space

The height of high-K domes will adjust according to the height of neutral buoyancy

(HNB) as dictated by material properties and temperature contrasts (Tan and Gur-

nis , 2005). To estimate the expected temperature differences we run a preliminary

BO model with the same parameters as BO5 (Table 5.2). An internal heating rate

H = 100 accounts for around 60% of the total heat flux. In the preliminary model,

the interior temperature of the domes reaches a steady-state T ≈ 0.83 (dimension-

ally ≈ 2800 K) but the ambient material temperature evolves as relatively cold slabs

accumulate at the CMB. At 250 Ma (model start time) the ambient material outside

of the domes has an average temperature of T = 0.5 and cools to T = 0.43 at the

present day. The assimilation method is not unduly affected by this cooling because

the efficient advection of slabs ensures that the uppermost mantle temperature re-

105

Table 5.2: Model-specific parameters. a Lithosphere and slab assimilation. b Thiscalculation assumes the domes are 1000 K hotter than ambient material, which isappropriate for the start of the model but evolves as slabs cool the mantle.Model Input Output

Approx Ra Assima δρch (%) δ K (%) mα ηC HNB (km)b

EX1 EX 1.83 × 108 Y 1.8 6 2 0 700EX2 EX 1.83 × 108 Y 1.9 9 3 0 700EX3 EX 1.83 × 108 Y 1.7 4 1 0 700BO1 BO 1.83 × 108 Y 1.8 6 2 0 700BO2 BO 1.83 × 108 Y 2.5 6 2 0 -BO3 BO 1.83 × 108 N 2.5 6 2 0 -BO4 BO 1.83 × 108 Y 2.5 6 2 100 -BO5 BO 1.83 × 108 Y B = 0.5 1 0 -BO6 BO 1.83 × 107 Y 2.5 6 2 0 -

mains close to T = 0.5. Rather, the dominant influence of this temperature change

is to increase the HNB. Mantle cooling will be less for the EX models because the

reduction in the thermal expansion coefficient with pressure will hinder the advection

of material and slabs will warm through diffusion. Nethertheless, this basic analysis

provides a convenient method to determine the likely evolution of high-K structures

without necessitating many expensive computations (Table 5.2).

Tan et al. (2011) generate high-K domes within a spherical geometry free-convection

model for density contrasts at the CMB between ≈ 1–2%. We anticipate requiring

upper values from this range for the domes to remain stable during 250 Myrs of

tectonic evolution.

5.3.5 Initial condition

Precalculations without data assimilation reveal that about 700 Myr is required for

high-K material to develop into high standing structures from an initial layer at the

106

CMB. At the start of our models (250 Ma) we therefore choose to prescribe two

domes centered on the equator at 0 and 180 degrees longitude (for the African and

Pacific structures) with a footprint that together occupies 20% of the CMB surface

area (Fig. 5.1b). The domes are essentially located in the present day position of

the LLSVPs, with the African structure marginally further north and the Pacific

structure displaced slighly west (Fig. 5.4a). For simplicity we define a height of 900

km for the domes and accept that this will adjust to the HNB (Fig. 5.4d). The total

volume of both structures is approximately 34.4×109 km3 which is comparable to the

volume of a 200-km-thick layer residing at the CMB. This volume is about a factor of

2 larger than estimates from seismic tomography (Burke et al., 2008; Hernlund and

Houser , 2008), but comparable to other geodynamic studies (McNamara and Zhong ,

2005; Zhang et al., 2010). Additionally, entrainment reduces the size of the structures

during the model run.

Ambient mantle is assigned a non-dimensional temperature T = 0.5 and in the

interior of the structures T = 0.8. This approach effectively assumes that most of the

domes existed as two coherent and relatively well-mixed structures prior to the early

Mesozoic. Thin thermal boundary layers (≈ 80 km) conduct heat from the CMB and

the top of the domes to ambient mantle. The thermal model for the lithosphere and

slabs is described in Section 5.3.3. Slabs are initially inserted from the surface to the

base of the transition zone (670 km depth).

107

60˚

120˚

180˚

-120˚

-60˚

presentl)

60˚

120˚

180˚

-120˚-6

50 Mak)

0.0 0.5 1.0

Temperature

60˚

120˚

180˚

-120˚

-60˚

100 Maj)

presenti)50 Mah)

-60˚ -60˚

0˚ 0˚

60˚ 60˚100 Mag)

60˚

120˚

180˚

-120˚

-60˚

150 Maf)

60˚

120˚

180˚

-120˚-6

200 Mae)

60˚

120˚

180˚

-120˚

-60˚

250 Mad)

150 Mac)200 Mab)

-60˚ -60˚

0˚ 0˚

60˚ 60˚250 Maa)

PAC

AFR

PAC

AFR

Figure 5.4: EX1 snapshots. (a, b, c, g, h, i) Temperature at 2600 km depth for250, 200, 150, 100, 50 Ma and present day, respectively. The compositionally distinctmaterial is contoured with black dashed lines. Ridges and transform faults are repre-sented by red lines and subduction zones are represented by black lines with sawteethindicating polarity. Reconstructed continent outlines are shown in light grey. (d, e,f, j, k, l) Equatorial annuli of temperature (0◦ is the Prime Meridian) for (a, b, c, g,h, i), respectively. “AFR” and “PAC” identify the domes.

108

5.4 Results

Fig. 5.4 illustrates the evolution of our reference model (EX1), which also encap-

sulates the key features of EX2 and EX3 (Table 5.2). During the initial 75 Myrs

the African structure is displaced northwards and the Pacific structure southwards

(Figs. 5.4a,b,c). The high-K structures retain their steep vertical walls and topog-

raphy on the interface is negligible. This demonstrates a posteriori that the initial

thermal and compositional structure for the domes (Fig. 5.4a,d) is dynamically com-

patible with the parameters of the calculations. Plate motions then shift both struc-

tures westward from ∼ 175 Ma to present day (Fig. 5.4g,h,i). The final position of

the African structure is beneath the Atlantic Ocean and South America, while the

Pacific structure is beneath the western Pacific Ocean and Australasia (Fig. 5.4i).

Neither dome experiences significant deformation since the initial prescribed ge-

ometry is largely retained. However, subducting slabs generate stresses that deflect

the top interface of the domes and can produce extensive topography. For example,

slabs originating from Central American subduction depress a western portion of the

African structure by several hundred kilometers (Fig. 5.4k,l, at -60◦). Circular em-

bayments punctuate the edge of the domes (Fig. 5.5, green arrows). These produce

tendrils of chemically distinct material that extend away from the structures and join

ridges of thickened boundary layer of ambient material (Fig. 5.5, red arrow). Slabs

are generally contained within the upper half of the mantle and do not accumulate

at the CMB.

Classical thermal plumes (spheroidal plume head followed by a tail) of ambient

109

Figure 5.5: Thermal plumes rising from ridges between the domes at present day(EX1). The T = 0.6 isosurface is coded by viscosity for depth perception (viscosityis pressure dependent). (a) View from the North Pole. The Pacific (PAC) andAfrican (AFR) structures are the prominent red-capped mesas. The contiguous bandof elevated temperature that is disconnected from the CMB is caused by dissipativeheating from Tethyan slabs (black arrows). (b) View centered on (90◦, 0◦) showing thewestern edge of the Pacific dome, circular embayments (green arrows), and tendrilsextending from the domes (red arrow)

110

material develop from interconnected ridges of thickened boundary layer at the CMB.

These are generally located away from the domes (Fig. 5.5) with more upwellings

beneath Africa and Eurasia than the Pacific region. The high-K structures develop

a perimeter of thickened boundary layer, although the edges are not prefered regions

of plume formation.

EX2 and EX3 have different drops in thermal expansion across the mantle (factor

of 3 and 1, respectively) and chemical density profiles compared to EX1. With a

comparable HNB these models are qualitatively similar to the reference model. The

domes in EX2 are marginally flatter with less edge deformation, and plume activity is

also reduced. Conversely, the structures in EX3 stand a little higher from the CMB

and have steeper sides. In this model, downwellings more significantly deform the

domes. For example, Central American slabs produce sufficient stresses to generate a

large circular embayment in the north of the African structure. To a lesser extent, dis-

placement of material away from Central America also occurs in EX1 (Fig. 5.4g,h,i).

The Boussinesq equivalent of EX1 (BO1) does not produce stable domes (Fig. 5.6).

Slabs are stronger in BO1 because they have more thermal buoyancy, and are therefore

cooler and more viscous at all mantle depths because the transit time through the

mantle is reduced (∼ 50 Myr). The slabs exert large stresses on the side walls of

the domes and can slide beneath the high-K structures, further destabilizing them.

Ultimately the domes rise off the CMB (Fig. 5.6f). In BO2, we increase the density

contrast at the CMB (δρch) whilst retaining the same bulk modulus anomaly. In

this model, the structures remain stable at the CMB until ∼ 70 Ma (Fig. 5.7c,e).

111

60˚

120˚

180˚

-120˚

-60˚

160 Maf)

60˚

120˚

180˚

-120˚-6

180 Mae)

0.0 0.5 1.0

Temperature

60˚

120˚

180˚

-120˚

-60˚

200 Mad)

160 Mac)180 Mab)

-60˚ -60˚

0˚ 0˚

60˚ 60˚200 Maa)

PAC

AFR

PAC

AFR

Figure 5.6: BO1 snapshots. (a, b, c) Temperature at 2600 km depth for 200, 180,160 Ma, respectively. (d, e, f) Equatorial annuli of temperature (0◦ is the PrimeMeridian) for (a, b, c), respectively. For details, see Fig. 5.4 caption.

Additionally, entrainment reduces the size of the domes, particularly the African

anomaly.

BO5 does not include a high-K component, but the evolution of the model from

250 to 70 Ma is similar to BO2 (compare Figs. 5.8h,k and Figs. 5.7c,e). In comparison

to BO2, BO5 achieves both stable domes and less entrainment (Fig. 5.8), although

the domes do not stand as high above the CMB and their edges are less steep. This is

particularly evident for the African anomaly. Nevertheless, in these cases the lateral

migration of the domes at the CMB is insensitive to the details of the chemically

distinct high-K or uniform density material. We therefore expect that BO5 is rep-

resentative of high-K models with stable domes and minimal entrainment, excluding

the vertical extent of the structures.

The domes initially flatten in BO5 because they are more dense than in the previ-

112

60˚

120˚

180˚

−120˚

−60

˚

70 Maf) BO3

60˚

120˚

180˚

−120˚

−60

˚

70 Mae) BO2

70 Mad) BO3

−60˚ −60˚

0˚ 0˚

60˚ 60˚70 Mac) BO2

170 Mab) BO3

−60˚ −60˚

0˚ 0˚

60˚ 60˚170 Maa) BO2

0.0 0.5 1.0

Temperature

AFR

PAC

PAC

AFR

Figure 5.7: BO2 (with assimilation) and BO3 (kinematic only) snapshots. Temper-ature at 2600 km depth for (a, c) BO2 at 170 and 70 Ma, respectively. (b, d) BO3at 170 and 70, respectively. (e, f) Equatorial annuli of temperature (0◦ is the PrimeMeridian) for (c, d), respectively. For details, see Fig. 5.4 caption.

113

60˚

120˚

180˚

-120˚

-60˚

presentl)

60˚

120˚

180˚

-120˚-6

50 Mak)

0.0 0.5 1.0

Temperature

60˚

120˚

180˚

-120˚

-60˚

100 Maj)

presenti)50 Mah)

-60˚ -60˚

0˚ 0˚

60˚ 60˚100 Mag)

60˚

120˚

180˚

-120˚

-60˚

150 Maf)

60˚

120˚

180˚

-120˚-6

200 Mae)

60˚

120˚

180˚

-120˚

-60˚

250 Mad)

150 Mac)200 Mab)

-60˚ -60˚

0˚ 0˚

60˚ 60˚250 Maa)

PAC

AFR

PAC

AFR

Figure 5.8: BO5 snapshots. (a, b, c, g, h, i) Temperature at 2600 km depth for250, 200, 150, 100, 50 Ma and present day, respectively. The compositionally distinctmaterial is contoured with black dashes. Ridges and transform faults are representedby red lines and subduction zones are represented by black lines with sawteeth indi-cating polarity. Reconstructed continent outlines are shown in light grey. (d, e, f, j,k, l) Equatorial annuli of temperature (0◦ is the Prime Meridian) for (a, b, c, g, h, i),respectively. For details, see Fig. 5.4 caption.

114

ous high-K models, which increases their CMB footprint throughout the model run.

Descending slabs promote thickening of the lower thermal boundary layer and a few

short-lived plumes develop at the edges of the domes. The domes deform readily in

response to slabs but have sufficient intrinsic density contrast to remain stable at the

CMB. They can develop steep edges from boundary tractions caused by slab-induced

flow (for example, the eastern edge of the Pacific anomaly, Fig. 5.8l, at -120◦). Else-

where the edges are tapered, such as the western boundary of the Pacific structure

(Fig. 5.8l, at 180◦).

In BO5, from 250 to 200 Ma, the African and Pacific structures are displaced

northwards and southwards, respectively, similar to EX1. Around 200 Ma the Pacific

dome is indented by western Pacific slabs that produce two embayments along its

boundary (Fig. 5.8b). Slabs from North and South America inhibit the African

structure from advancing west while slabs from Africa-Eurasian collision displace

material from North Africa (Fig. 5.8c). This elongates the African dome north-south

in the northern hemisphere and west-east in the southern hemisphere. The African

structure migrates slightly westward as seafloor spreading in the South Atlantic Ocean

moves Africa northeastward (Fig. 5.8h). During this time slabs continue to pile up

beneath present day Africa (Fig. 5.8i). The Pacific structure is slightly elongated

north-south by circum-Pacific slabs from 100 Ma and is centrally located beneath the

Pacific Ocean at present (Fig. 5.8i).

Central American slabs slice a small region from the African structure around 230

Ma (small structure to the southwest of the main African anomaly in Fig. 5.8b). This

115

material migrates southwestward and eventually merges with the Pacific structure at

∼ 200 Ma. Additionally, the African dome develops a limb at 200 Ma that extends

beneath northwest North America (Fig. 5.8c). This extension merges with the north-

west boundary of the Pacific dome around 140 Ma, and slabs eventually detach the

limb from the main African structure at 100 Ma.

Geodynamic studies often apply a purely kinematic boundary condition to the

top surface of models to produce downwellings at convergent plate margins. However,

with this approach it is not clear if the downgoing buoyancy flux is reasonable for

the convergence rate and lithospheric buoyancy predicted by geologically consistent

plate reconstructions. Therefore, we compare the influence of lithosphere and slab

assimiliation (BO2) with a purely kinematic boundary on the top surface (BO3)

(Fig. 5.7); all model parameters are otherwise identical. The assimilation method

increases slab flux into the lower mantle and the domes have steeper sides and reduced

volume.

McNamara and Zhong (2004) demonstrate that an intrinsic viscosity increase in

the chemically distinct material can control the style of deformation of the domes. In

comparison to BO2, the domes in BO4 have a factor 100 intrinsic viscosity increase.

The first downwellings to reach the CMB perturb the lower thermal boundary and

generate plumes both at the edges of the domes and away from the structures. From

250 Ma to present, the domes remain as individual coherent structures and do not

exchange mass between each other. The topography on the top of the domes is largely

unperturbed. At present, the domes are located similarly to BO5 (Fig. 5.8i), except

116

the African structure is more localized beneath the South Atlantic Ocean and South

America and the Pacific structure is rounder.

A reduced Rayleigh number (Ra = 1.83× 107) decreases the sinking rate of slabs

because it is equivalent to increasing the background viscosity uniformly (BO6). Con-

vection is more sluggish and its characteristic length-scale larger. From 250 to 150

Ma, the evolution of BO6 is akin to EX1 (Fig. 5.8i) where the domes migrate north

and south for the African and Pacific structures, respectively. Around 110 Ma, Cen-

tral American slabs carve a portion of the African structure which merges with the

Pacific dome at ∼ 80 Ma. This is similar to the behavior in BO5 although the

timescale is increased for the lower Ra model. At present, the African structure is

elongated north-south and located beneath the Atlantic Ocean with its eastern margin

roughly following the African coastline. The Pacific structure is stretched west-east

and located beneath the Pacific Ocean, although preferentially to the west.

5.5 Discussion

The models broadly fall into two classes, depending on whether the domes are pre-

dominantly affected by the buoyancy of subducting slabs or by coupling to surface

plate motions. The EX models are dominated by coupling to plates and slab buoy-

ancy is weak (“weak-slab models”). In contrast, the BO models are most influenced

by downwellings that accumulate at the CMB (“strong-slab models”).

At present day the high-K structures are marginally flatter in EX2 and steeper-

sided in EX3, relative to EX1. Nevertheless, for the weak-slab models, each dome

117

-60˚ -60˚

0˚ 0˚

60˚ 60˚

kinematicd) BO3

-60˚ -60˚

0˚ 0˚

60˚ 60˚

c) BO6

-60˚ -60˚

0˚ 0˚

60˚ 60˚

b) BO5

-60˚ -60˚

0˚ 0˚

60˚ 60˚

a) EX1

0 50 100 150 200 250

Age (Ma)

Figure 5.9: Motion and deformation of the domes at 2600 km depth, (a) EX1, (b)BO5, (c) BO6, (d) BO3. The grey-shaded region shows the domes at present dayand the dark grey dashes contour the initial position of the domes at 250 Ma. Blackdashes delineate the -0.6% S-wave contour from SB10L18 and continent outlines areshown in solid dark grey. Color-coded dots show the movement of the domes from250 Ma to present day.

118

follows a similar course as it migrates along the CMB and its present day location is

comparable (Fig. 5.9a). From 250 to 150 Ma, the African and Pacific structures move

to the north and south, respectively. Dominant motion is then westward from 150

Ma to present day. Both domes are displaced between 35◦ (Pacific) and 45◦ (African)

west of their initial position at 250 Ma. The Pacific dome lies beneath many of

the western Pacific subduction zones, which seems contrary to the hypothesis that

chemical layers are displaced away from downwellings (Davies and Gurnis , 1986;

McNamara and Zhong , 2005). However, domes may exist beneath subduction zones

if they have only recently initiated. For example, Tonga overlies the edge of the Pacific

LLSVP, but is relatively young, having only formed since 45 Ma (Gurnis et al., 2000).

A weak slab push force does not overly influence the morphology and location of the

structures. Therefore the high-K structures are stable and generally coherent with

sharp steep walls, similar to models without slabs (Tan and Gurnis , 2005, 2007).

However, downwellings can generate significant topography on the domes and locally

displace material from some regions of the CMB.

Slabs in the strong-slab models with lithosphere and slab assimilation can prop-

agate to the CMB and deform and displace the domes. From 250 to 200 Ma, the

Paleo-Tethys seafloor is relatively old and introduces a large amount of negative buoy-

ancy into the mantle at the trench through slab assimilation. This is compounded by

the Tethyan/Mongol-Okhotsk triple junction (trench-trench-trench) (Fig. 5.2), and

slabs pile up on the CMB and push material southwestward toward (and ultimately

beyond) present day Africa (Fig. 5.9b). This deforms the African structure into an

119

elongated kidney shape that migrates southwestward after the opening of the South

Atlantic Ocean. By contrast, the seafloor is generally younger at the North and South

America trenches and the assimilated slabs have less negative buoyancy and a smaller

viscosity contrast. Therefore these slabs are weaker and unable to counter the mo-

tion of the African dome to the southwest caused by Tethyan slabs. Nevertheless,

the ridge-like morphology of the African structure agrees with tomography (Fig. 5.1),

waveform modeling (Ni and Helmberger , 2003b), and other geodynamic studies (e.g.,

McNamara and Zhong , 2005).

The Pacific structure migrates eastward in the strong slab models, which contrasts

with predominant westward motion in the weak-slab models (Fig. 5.9a,b). This is

because slabs from the western Pacific subduction zones are dominant in pushing the

dome beneath the Pacific Ocean. Tomographic inversions suggest that the basic mor-

phology of this structure is a rounded pile slightly elongated in longitude (Fig. 5.1).

Our Pacific dome is generally well located, although slightly extended in the latitudi-

nal direction. This implies that slabs originating from subduction zones in the north

and south Pacific (versus the west and east margins) are less dominant in shaping

the boundaries of the dome.

A purely kinematic surface boundary condition (BO3) displaces and deforms the

domes similarly to models with lithosphere and slab assimilation (Figs. 5.9b,d). In

BO3, the African and Pacific structures align more closely with tomography and

the Pacific structure is enlongated west–east. However, the vertical extent of the

structures varies significantly despite the same high-K parameters (Fig. 5.7). The

120

79 Ma

0 200Seafl oor age (Ma) 0 1Temperature

79 Ma

Present

Present

a) AFR b) AFR

c) PAC d) PAC

Figure 5.10: 3-D view of the domes in model BO5. African structure at (a) 79 Ma,(b) Present. Pacific structure at (c) 79 Ma, (d) Present. Ridges and transform faultsare represented by red lines and subduction zones are represented by black lines.Non-oceanic regions are dark grey and reconstructed continents with present dayshorelines are shown in white.

121

assimilation method increases the down flux into the lower mantle, which has two

main effects. First, the stronger slab push steepens the boundaries of the domes.

Second, the lower mantle is more efficiently cooled, which raises the HNB of the

high-K structures. Therefore, with realistic slab fluxes we expect high-K structures

to be less stable than the prediction from models with purely kinematic boundary

conditions.

Domes with increased intrinsic viscosity (BO4) do not deform readily in response

to slabs, retain a relatively flat top, and become hotter because convection is inhibited

(McNamara and Zhong , 2004). However, the lateral motion of the structures is not

unduly affected because of the free-slip boundary condition at the CMB.

For BO6 (Ra = 1.83 × 107), the shape and areal extent of the domes at 2600 km

depth correlate fairly well to tomography (Fig. 5.9c). The African structure is dis-

placed too far west although the mismatch is less than for the other models. A sliver

of the African dome is carved from the main anomaly by slabs from Central Amer-

ican subduction, which eventually merges with the eastern boundary of the Pacific

structure (Fig. 5.9c, leftmost tracer). This demonstrates how mass transfer between

the domes (McNamara et al., 2010) may be intimately linked to paleogeography.

The “weak-slab models” arise from the extended-Boussinesq approximation. Adi-

abatic and viscous heating are often ignored in convection calculations because they

are in balance globally (e.g., Leng and Zhong , 2008). However, even though some pre-

vious studies neglect these terms (McNamara and Zhong , 2005; Zhang et al., 2010;

Steinberger and Torsvik , 2011) they contribute significantly to dissipate the ther-

122

mal anomaly of slabs in our EX models. It is uncertain how these dissipative terms

interact with model parameters and data assimilation.

Steinberger and Torsvik (2011) (hereafter ST11) recently developed a geodynamic

model to investigate plume formation at the edges of the domes by prescribing a slab

buoyancy flux constrained by global plate reconstructions. BO6 has a comparable

Rayleigh number to ST11, yet the location of their domes at the CMB agrees better

with seismic tomography. We attribute the difference to two major factors.

First, ST11 apply the plate model to determine the depth-integrated density

anomaly of oceanic lithosphere at the trench. This truncates the maximum slab

buoyancy to the equivalent of 80 Ma seafloor, whereas our half-space model includes

more buoyancy for older slabs. ST11 further reduce slab buoyancy by 21% to account

for the subduction of crust and depleted mantle. This means their slab buoyancy is

significantly reduced for all subduction zones, and particularly those with subducting

plates older than 80 Ma (noteably the Tethyan region at certain ages). The plate

model therefore likely mitigates the Tethyan slab push that migrates the African

dome in our models to the southwest.

Second, the location of paleosubduction influences the evolution of the domes.

The subduction models used in ST11 (Steinberger and Torsvik , 2010) and this study

(Seton et al., 2012) appear qualitatively similar, but it remains unknown how the

evolution of specific regions affects the deep-Earth structure. ST11 also apply a

longitudinal shift to subduction zone locations (van der Meer et al., 2010) which

improves their dome fit to tomography. Applying a similar rotation to our plate

123

0 50 100 150 200 250

Age (Ma)

0 4 8 12 16

Sinking speed (cm/yr)

0

400

800

1200

1600

2000

2400

2800

Dep

th (

km

)

20 21 22 23 24

log10 (viscosity (Pas))

EX1 (present)

BO2 (70 Ma)

BO3 (70 Ma)

BO5 (present)

BO6 (present)

a) b) c)

Figure 5.11: Radial profiles for (a) Viscosity, (b) Slab sinking speed, (c) Approximateage of subducted material versus depth, for EX1, BO5, BO6 at present day, and BO5,BO6 at 70 Ma. Sinking speed is determined from positive density anomalies that aregreater than 25% of the maximum positive density anomaly at each depth and time(e.g., Steinberger and Torsvik , 2010). We set the velocities for depths < 128 km tothe value at 128 km depth because they are influenced by data assimilation. Theage-depth relation is computed by integrating the time- and depth-dependent slabsinking speed.

history model may enforce the migration of the African dome to the southwest and

increase the mismatch.

The slab sinking rate for most of the models here is larger than geological esti-

mates (e.g., 1.2 cm yr−1, van der Meer et al., 2010), except for BO6 (Fig. 5.11c). BO6

has a lower Rayleigh number, which is equivalent to a ubiquitous increase in mantle

viscosity (Fig. 5.11a). The Stokes sinking velocity is proportional to the driving den-

sity contrast and inversely proportional to the background viscosity. Slabs in EX1

124

do not retain a strong thermal anomaly for depths > 1400 km because the temper-

ature anomaly is dissipated (Fig. 5.11b). BO2 (with assimilation) and BO3 (purely

kinematic) at 70 Ma have approximately the same age-depth relation (Fig. 5.11c),

despite the significantly increased lower-mantle slab flux from slab assimilation. This

is because cooler material in the lower mantle reduces the driving density contrast

for subsequent downwellings. Furthermore, the bulk background viscosity increases

through the temperature-dependent rheology, which further reduces the sinking veloc-

ity of slabs (Fig. 5.11a). BO3 actually has a marginally faster sinking rate throughout

the lower mantle.

We observe plumes forming at the edges of the domes (Tan et al., 2011; Steinberger

and Torsvik , 2011) from thickened boundary layer pushed toward the structures by

slabs. However, plume formation is partly controlled by the maturity (thermal buoy-

ancy available at the CMB) and stability of the lower thermal boundary. Since the

most prominant edge-activity occurs during the early stage of the model we relate this

largely to the initial condition and the lack of preexisting plume conduits. Further-

more, a 250 Myr integration time is not sufficient for a statistical analysis of plume

distribution.

For the high-K structures in the strong-slab models (BO2, BO3, BO4, BO6), the

chemical density anomaly is larger than the thermal density anomaly across the whole

mantle pressure range. Therefore a HNB does not exist and the high-K material effec-

tively replicates a high-density layer. We consider the density anomaly at the CMB

(relative to ambient material) for high-K material, ∆ρk, and slab, ∆ρs. High-K struc-

125

tures form when ∆ρk < 0, and to ensure they remain stable in the presence of slabs

requires ∆ρk > ∆ρs. However the latter relation cannot be true because ∆ρs > 0.

Therefore, slabs will always have a tendancy to sweep beneath high-K structures un-

less ∆ρk is large and thermal buoyancy no longer dominates at depth. Furthermore,

the hot domes have low viscosity and therefore deform readily in response to stresses

from stiffer slabs. This further enables slabs to compromise stability by sliding be-

neath the domes. Higher intrinsic viscosity for the high-K structures can mitigate

this effect (BO4).

5.6 Conclusions

We present models that investigate the stability and morphology of high bulk modulus

structures in the lower mantle from 250 Ma to present day with constraints from pale-

ogeography. The domes in “weak-slab” models are strongly coupled to plate motions

and migrate along the CMB as coherent structures without significant deformation.

These structures are displaced 35 to 45 degrees west of their inferred position from

seismic tomography. In contrast, the domes in ‘strong slab’ models deform and mi-

grate along the CMB in response to slab stresses. These models produce a ridge-like

anomaly beneath Africa and a rounded pile beneath the Pacific Ocean, similar to

previous studies. However, the African structure is displaced too far southwest in

comparison to seismic modeling. This is because the progressive assimilation method

produces strong Tethyan slabs that deform the African dome into a kidney shape and

displace the structure to the southwest beyond present-day Africa.

126

High-K structures rely on a delicate dynamic balance between thermal and chem-

ical buoyancy; they are almost neutrally buoyant because net density differences are

small. Therefore, high-K domes are passive components and the flow is largely im-

posed by plate motions and slabs. Even “weak slabs” produce notable topography

on the surface of the high-K structures and can locally displace material from some

downwelling regions (e.g., Central America). “Strong slabs” that are more dense and

more viscous than the structures generate stresses that can compromise the stability

of the domes at the CMB. Additionally, these slabs can further steepen the edges of

high-K structures (or uniform dense layers) and may slide beneath the domes, which

can cause the structures to raise off the CMB. Relative to models without slabs, the

parameter space for stable high-K structures appears to be reduced.

Finally, our study also outlines a new modeling framework to utilize paleogeog-

raphy constraints from plate history models to chart the evolution of deep mantle

structures. This modeling suggests that the assimilation method increases the slab

buoyancy flux relative to models with a purely kinematic boundary condition on the

top surface.

127

Appendix A

Derivation of the mineral physics

derivatives

128

We use the same notation as presented in Chapter 2. Subscripts pv and ppv denote

the perovskite (Pv) and post-perovskite (pPv) phase, respectively.

δvp =1

2

(

δK + 4R1δG/3

1 + 4R1/3− δρ

)

(A.1)

δvs =1

2(δG − δρ). (A.2)

For Pv:

δKpv =∂lnK

∂TdT (A.3)

δGpv =∂lnG

∂TdT (A.4)

δρpv = −ραα0dT∆T (A.5)

where dT is a (non-dimensional) temperature perturbation from a reference state.

For pPv:

δKppv = δKpv +∂lnK

∂Γ(A.6)

δGppv = δGpv +∂lnG

∂Γ(A.7)

δρppv = δρpv +Rb

Raα0∆T (A.8)

δvpppv =1

2

(

δKpv + 4R1δGpv/3

1 + 4R1/3− δρpv +

∂lnK∂Γ

+ 4R1∂lnG∂Γ

/3

1 + 4R1/3−

Rb

Raα0∆T

)

(A.9)

δvsppv = 1/2

(

δGpv − δρpv +∂lnG

∂Γ−

Rb

Raα0∆T

)

. (A.10)

Considering the fractional increase in the S- and P-wave velocities across the Pv-pPv

129

phase transition:

δvpppv = δvppv + δvpΓ (A.11)

δvsppv = δvspv + δvsΓ (A.12)

where δvsΓ and δvpΓ are the fractional perturbations to the S- and P-wave velocity,

respectively, due to the Pv-pPv phase transition. By substitution:

∂lnG

∂Γ= 2δvsΓ +

Rb

Raα0∆T (A.13)

∂lnK

∂Γ=

(

2δvpΓ +Rb

Raα0∆T

)

(1 + 4R1/3) − 4R1/3∂lnG

∂Γ. (A.14)

130

Bibliography

Akber-Knutson, S., G. Steinle-Neumann, and P. D. Asimow (2005), Effect of Al on the

sharpness of the MgSiO3 perovskite to post-perovskite phase transition, Geophys.

Res. Lett., 32 (14), L14,303, doi:10.1029/2005GL023192.

Ammann, M. W., J. P. Brodholt, and D. P. Dobson (2009), DFT study of mi-

gration enthalpies in MgSiO3 perovskite, Phys. Chem. Miner., 36, 151–158, doi:

10.1007/S0029-008-0265-Z.

Ammann, M. W., J. P. Brodholt, J. Wookey, and D. P. Dobson (2010), First-principles

constraints on diffusion in lower-mantle minerals and a weak D′′ layer, Nature, 465,

462–465, doi:10.1038/nature09052.

Andrault, D., M. Munoz, N. Bolfan-Casanova, N. Guignot, J.-P. Perrillat,

G. Aquilanti, and S. Pascarelli (2010), Experimental evidence for perovskite and

post-perovskite coexistence throughout the whole D′′ region, Earth Planet. Sc.

Lett., 293 (1–2), 90–96, doi:10.1016/j.epsl.2010.02.026.

Auzende, A.-L., J. Badro, F. J. Reyerson, P. K. Weber, S. J. Fallon, A. Addad,

J. Siebert, and G. Fiquet (2008), Element partitioning between magnesium silicate

131

perovskite and ferropericlase: New insights into bulk lower-mantle geochemistry,

Earth Planet. Sc. Lett., 269, 164–174, doi:10.1016/j.epsl.2008.02.001.

Avants, M., T. Lay, and E. J. Garnero (2006), A new probe of ULVZ S-wave velocity

structure: Array stacking of ScS waveforms, Geophys. Res. Lett., 33, L07314, doi:

10.1029/2005GL024989.

Badro, J., G. Fiquet, F. Guyot, J.-P. Rueff, V. V. Struzhkin, G. Vanko, and

G. Monaco (2003), Iron partitioning in Earth’s mantle: Toward a deep lower mantle

discontinuity, Science, 300, 789–791, doi:10.1126/science.1081311.

Badro, J., J.-P. Rueff, G. Vanko, G. Monaco, G. Fiquet, and F. Guyot (2004), Elec-

tronic transitions in perovskite: Possible nonconvecting layers in the lower mantle,

Science, 305, 383–386, doi:10.1126/science.1098840.

Berryman, J. G. (2000), Seismic velocity decrement ratios for regions of partial melt in

the lower mantle, Geophys. Res. Lett., 27 (3), 421–424, doi:10.1029/1999GL008402.

Billen, M. I., and G. Hirth (2007), Rheologic controls on slab dynamics, Geochem.

Geophy. Geosy., 8 (8), Q08012, doi:10.1029/2007GC001597.

Burke, K., and T. H. Torsvik (2004), Derivation of large igneous provinces of the past

200 million years from long-term heterogeneities in the deep mantle, Earth Planet.

Sc. Lett., 227 (c), 531–538, doi:10.1016/j.epsl.2004.09.015.

Burke, K., B. Steinberger, T. H. Torsvik, and M. A. Smethurst (2008), Plume gener-

132

ation zones at the margins of large low shear velocity provinces on the coremantle

boundary, Earth Planet. Sc. Lett., 265, 49–60, doi:10.1016/j.epsl.2007.09.042.

Byerlee, J. D. (1978), Friction of rocks, Pure Appl. Geophys., 116 (4–5), 615–626,

doi:10.1007/BF00876528.

Catalli, K., S.-H. Shim, and V. Prakapenka (2010), Thickness and Clapey-

ron slope of the post-perovskite boundary, Nature, 463 (7279), 384–384, doi:

10.1038/nature08770.

Christensen, U. (1984), Instability of a hot boundary layer and initiation of thermo-

chemical plumes, Ann. Geophys., 2 (3), 311–320.

Christensen, U. R., and D. A. Yuen (1985), Layered convection induced by phase tran-

sitions, J. Geophys. Res., 90 (B12), 10,291–10,300, doi:10.1029/JB090iB12p10291.

Cleary, J. R. (1974), The D′′ region, Phys. Earth Planet. In., 9, 13–27, doi:

10.1016/0031-9201(74)90076-4.

Cleary, J. R., and R. A. W. Haddon (1972), Seismic wave scattering near the core-

mantle boundary: A new interpretation of precursors to PKP, Nature, 240, 549–

551, doi:10.1038/240549a0.

Crowhurst, J., J. Brown, A. Goncharov, and S. Jacobsen (2008), Elasticity of

(Mg,Fe)O through the spin transition of iron in the lower mantle, Science, 319,

doi:10.1126/science.1149606.

133

Davies, G. F. (1999), Dynamic Earth: plates, plumes, and mantle convection, Cam-

bridge University Press.

Davies, G. F., and M. Gurnis (1986), Interaction of mantle dregs with convection:

lateral heterogeneity at the core-mantle boundary, Geophys. Res. Lett., 13 (13),

1517–1520.

de Koker, N. (2010), Thermal conductivity of MgO periclase at high pressure:

Implications for the D′′ region, Earth Planet. Sc. Lett., 292, 392–398, doi:

10.1016/j.epsl.2010.02.011.

Ding, X., and D. V. Helmberger (1997), Modelling D′′ structure beneath Central

America with broadband seismic data, Phys. Earth Planet. In., 101, 245–270, doi:

10.1016/S0031-9201(97)00001-0.

Dobson, D. P., and J. P. Brodholt (2005), Subducted banded iron formations as a

source of ultralow-velocity zones at the core-mantle boundary, Nature, 434, 371–

374, doi:10.1038/nature03385.

Dubrovinsky, L. S., N. A. Dubrovinskaia, S. K. Saxena, H. Annersten, E. Halenius,

H. Harryson, F. Tutti, S. Rekhi, and T. Le Bihan (2000), Stability of ferropericlase

in the lower mantle, Science, 289 (5478), 430–432, doi:10.1126/science.289.5478.430.

Dziewonski, A., and D. L. Anderson (1981), Preliminary reference Earth model, Phys.

Earth Planet. In., 25 (4), 297–356, doi:10.1016/0031-9201(81)90046-7.

Fei, Y., L. Zhang, A. Corgne, H. Watson, A. Riccolleau, Y. Meng, and V. Prakapenka

134

(2007), Spin transition and equations of state of (Mg,Fe)O solid solutions, Geophys.

Res. Lett., 34, L17307, doi:10.1029/2007GL030712.

Flores, C., and T. Lay (2005), The trouble with seeing double, Geophys. Res. Lett.,

32, L24305, doi:10.1029/2005GL024366.

Garnero, E. J., and D. V. Helmberger (1995), A very slow basal layer underlying large-

scale low-velocity anomalies in the lower mantle beneath the Pacific: evidence from

core phases, Phys. Earth Planet. In., 91, 161–176, doi:10.1016/0031-9201(95)03039-

Y.

Garnero, E. J., and D. V. Helmberger (1996), Seismic detection of a thin laterally

varying boundary layer at the base of the mantle beneath the central-Pacific, Geo-

phys. Res. Lett., 23 (9), 977–980, doi:10.1029/95GL03603.

Garnero, E. J., and D. V. Helmberger (1998), Further structural constraints and

uncertainties of a thin laterally varying ultralow-velocity layer at the base of the

mantle, J. Geophys. Res., 103 (B6), 12,495–12,509, doi:10.1029/98JB00700.

Garnero, E. J., and A. K. McNamara (2008), Structure and dynamics of Earth’s lower

mantle, Science, 320, 626–628, doi:10.1126/science.1148028.

Garnero, E. J., and J. E. Vidale (1999), ScP; a probe of ultralow velocity

zones at the base of the mantle, Geophys. Res. Lett., 26 (3), 377–380, doi:

10.1029/1998GL900319.

Garnero, E. J., D. V. Helmberger, and S. Grand (1993a), Preliminary evidence for a

135

lower mantle shear wave velocity discontinuity beneath the central Pacific, Phys.

Earth Planet. In., 79, 335–347, doi:10.1016/0031-9201(93)90113-N.

Garnero, E. J., S. P. Grand, and D. V. Helmberger (1993b), Low P-wave ve-

locity at the base of the mantle, Geophys. Res. Lett., 20 (17), 1843–1846, doi:

10.1029/93GL02009.

Glatzmaier, G. A., and P. H. Roberts (1995), A three-dimensional convective dynamo

solution with rotating and finitely conducting inner core and mantle, Phys. Earth

Planet. In., 91, 63–75, doi:10.1016/0031-9201(95)03049-3.

Goncharov, A. F., B. D. Haugen, V. V. Struzhkin, P. Beck, and S. D. Jacobsen

(2008), Radiative conductivity in the Earth’s lower mantle, Nature, 456, doi:

10.1038/nature07412.

Grand, S. P. (2002), Mantle shear-wave tomography and the fate of subducted slabs,

Phil. Trans. R. Soc. Lond. A, 360 (1800), 2475–2491, doi:10.1098/rsta.2002.1077.

Gurnis, M., J. Ritsema, H.-J. van Heijst, and S. Zhong (2000), Tonga slab deforma-

tion: The influence of a lower mantle upwelling on a slab in a young subduction

zone, Geophys. Res. Lett., 27, 2373–2376, doi:10.1029/2000GL011420.

Gurnis, M., et al. (2012a), Plate tectonic reconstructions with continuously closing

plates, Comput. Geosci., 38, 35–42, doi:10.1016/j.cageo.2011.04.014.

Gurnis, M., D. J. Bower, and N. Flament (2012b), Assimilating lithosphere and slab

history in 4-D dynamic Earth models, in preparation.

136

Hama, J., and K. Suito (2001), Thermoelastic models of minerals and the compo-

sition of the Earth’s lower mantle, Phys. Earth Planet. In., 125 (1–4), 147–166,

doi:10.1016/S0031-9201(01)00248-5.

Hansen, U., and D. A. Yuen (1988), Numerical simulations of thermal-chemical insta-

bilities at the core-mantle boundary, Nature, 334, 237–240, doi:10.1038/334237a0.

Hansen, U., D. A. Yuen, and S. E. Kroening (1991), Effects of depth-dependent

thermal expansivity on mantle circulations and lateral thermal anomalies, Geophys.

Res. Lett., 18 (7), 1261–1264, doi:10.1029/91GL01288.

Hansen, U., D. Yuen, S. Kroening, and T. Larsen (1993), Dynamical consequences

of depth-dependent thermal expansivity and viscosity on mantle circulations

and thermal structure, Phys. Earth Planet. In., 77, 205–223, doi:10.1016/0031-

9201(93)90099-U.

Havens, E., and J. Revenaugh (2001), A broadband seismic study of the lowermost

mantle beneath Mexico: constraints on ultralow velocity zone elasticity and density,

J. Geophys. Res., 106 (B12), 30,809–30,820, doi:10.1029/2000JB000072.

He, Y., and L. Wen (2009), Structural features and shear-velocity structure of the

“Pacific Anomaly”, J. Geophys. Res., 114, B02309, doi:10.1029/2008JB005814.

He, Y., L. Wen, and T. Zheng (2006), Geographic boundary and shear wave velocity

structure of the “Pacific anomaly” near the core-mantle boundary beneath western

Pacific, Earth Planet. Sc. Lett., 244, 302–314, doi:10.1016/j.epsl.2006.02.007.

137

Heine, C., R. D. Muller, and C. Gaina (2004), Reconstructing the lost eastern Tethys

Ocean basin: Constraints for the convergence history of the SE Asian margin

and marine gateways, in Continent-Ocean Interactions within East Asian Marginal

Seas, Geophys. Monogr. Ser., Vol. 149, edited by P. Clift, P. Wang, W. Kuhnt, and

D. Hayes, pp. 37–54, AGU, Washington, D.C., doi:10.1029/GM149.

Helmberger, D., S. Ni, L. Wen, and J. Ritsema (2000), Seismic evidence for ultralow-

velocity zones beneath Africa and the eastern Atlantic, J. Geophys. Res., 105 (B10),

23,865–23,878, doi:10.1029/2000JB900143.

Helmberger, D. V., and S. Ni (2005), Seismic modeling constraints on the South

African super plume, in Earth’s Deep Mantle: Structure, Composition, Evolution,

Geophys. Monogr. Ser., Vol. 160, edited by R. D. van der Hilst, J. D. Bass, J. Matas,

and J. Trampert, pp. 63–81, AGU, Washington, D.C., doi:10.1029/160GM06.

Helmberger, D. V., E. J. Garnero, and X. Ding (1996), Modeling two-dimensional

structure at the core-mantle boundary, J. Geophys. Res., 101 (B6), 13,963–13,972,

doi:10.1029/96JB00534.

Helmberger, D. V., L. Wen, and X. Ding (1998), Seismic evidence that the source

of the Iceland hotspot lies at the core-mantle boundary, Nature, 396, 251–255,

doi:10.1038/24357.

Hernlund, J. W., and C. Houser (2008), On the statistical distribution of seismic

velocities in Earth’s deep mantle, Earth Planet. Sc. Lett., 265, 423–437, doi:

10.1016/j.epsl.2007.10.042.

138

Hernlund, J. W., and A. M. Jellinek (2010), Dynamics and structure of a stirred

partially molten ultralow-velocity zone, Earth Planet. Sc. Lett., 296 (1–2), 1–8,

doi:10.1016/j.epsl.2010.04.027.

Hernlund, J. W., and S. Labrosse (2007), Geophysically consistent values of the

perovskite to post-perovskite transition Clapeyron slope, Geophys. Res. Lett., 34,

L05309, doi:10.1029/2006GL028961.

Hernlund, J. W., and P. J. Tackley (2007), Some dynamical consequences of par-

tial melting in Earth’s deep mantle, Phys. Earth Planet. In., 162, 149–163, doi:

10.1016/j.pepi.2007.04.005.

Hernlund, J. W., C. Thomas, and P. J. Tackley (2005), A doubling of the post-

perovskite phase boundary and structure of the Earth’s lowermost mantle, Nature,

434, 882–886, doi:10.1038/nature03472.

Hier-Majumder, S. (2008), Influence of contiguity on seismic velocities of partially

molten aggregates, J. Geophys. Res., 113, B12205, doi:10.1029/2008JB005662.

Hier-Majumder, S., and J. Revenaugh (2010), Relationship between the viscosity and

topography of the ultralow-velocity zone near the core-mantle boundary, Earth

Planet. Sc. Lett., 299 (3–4), 382–386, doi:10.1016/j.epsl.2010.09.018.

Hirose, K., R. Sinmyo, N. Sata, and Y. Ohishi (2006), Determination of post-

perovskite phase transition boundary in MgSiO3 using Au and MgO pressure stan-

dards, Geophys. Res. Lett., 33 (1), L01310, doi:10.1029/2005GL024468.

139

Hofmeister, A. M. (1999), Mantle values of thermal conductivity and the geotherm

from phonon lifetimes, Science, 283, 1699–1706, doi:10.1126/science.283.5408.1699.

Hofmeister, A. M. (2008), Inference of high thermal transport in the lower mantle

from laser-flash experiments and the damped harmonic oscillator model, Phys.

Earth Planet. In., 170, 201–206, doi:10.1016/j.pepi.2008.06.034.

Hutko, A. R., T. Lay, E. J. Garnero, and J. Revenaugh (2006), Seismic detection of

folded, subducted lithosphere at the core-mantle boundary, Nature, 441, 333–336,

doi:10.1038/nature04757.

Hutko, A. R., T. Lay, J. Revenaugh, and E. J. Garnero (2008), Anticorrelated seismic

velocity anomalies from post-perovskite in the lowermost mantle, Science, 320,

1070–1074, doi:10.1126/science.1155822.

Hutko, A. R., T. Lay, and J. Revenaugh (2009), Localized double-array stack-

ing analysis of PcP: D′′ and ULVZ structure beneath the Cocos Plate, Mex-

ico, Central Pacific and North Pacific, Phys. Earth Planet. In., 173, 60–74, doi:

10.1016/j.pepi.2008.11.003.

Idehara, K., A. Yamada, and D. Zhao (2007), Seismological constraints on the ul-

tralow velocity zones in the lowermost mantle from core-reflected waves, Phys.

Earth Planet. In., 165, 25–46, doi:10.1016/j.pepi.2007.07.005.

Iitaka, T., K. Hirose, K. Kawamura, and M. Murakami (2004), The elasticity of the

MgSiO3 post-perovskite phase in the Earth’s lowermost mantle, Nature, 430 (6998),

442–445, doi:10.1038/nature02702.

140

Irifune, T. (1994), Absence of an aluminous phase in the upper part of the Earth’s

lower mantle, Nature, 370, 131–133, doi:10.1038/370131a0.

Ishii, M., and J. Tromp (1999), Normal-mode and free-air gravity constraints on

lateral variations in velocity and density of Earth’s mantle, Science, 285, 1231–

1236, doi:10.1126/science.285.5431.1231.

Ishii, M., and J. Tromp (2004), Constraining large-scale mantle heterogeneity using

mantle and inner-core sensitive normal modes, Phys. Earth Planet. In., 146 (1–2),

113–124, doi:10.1016/j.pepi.2003.06.012.

Ita, J., and S. D. King (1994), Sensitivity of convection with an endothermic phase

change to the form of the governing equations, initial conditions, boundary con-

ditions, and equation of state, J. Geophys. Res., 99 (B8), 15,919–15,938, doi:

10.1029/94JB00852.

Jackson, J. M., J. Zhang, J. Shu, S. V. Sinogeikin, and J. D. Bass (2005), High-

pressure sound velocities and elasticity of aluminous MgSiO3 perovskite to 45 GPa:

Implications for lateral heterogeneity in Earth’s lower mantle, Geophys. Res. Lett.,

32, L21305, doi:10.1029/2005GL023522.

Jarvis, G. T., and D. P. McKenzie (1980), Convection in a compressible

fluid with infinite Prandtl number, J. Fluid Mech., 96 (3), 515–583, doi:

10.1017/S002211208000225X.

Jellinek, A. M., and M. Manga (2002), The influence of a chemical boundary layer

141

on the fixity, spacing and lifetime of mantle plumes, Nature, 418, 760–763, doi:

10.1038/nature00979.

Karato, S., and B. B. Karki (2001), Origin of lateral variation of seismic wave veloc-

ities and density in the deep mantle, J. Geophys. Res., 106 (B10), 21,771–21,783.

Karato, S.-I., and P. Li (1992), Diffusion creep in perovskite: Implications

for the rheology of the lower mantle, Science, 255 (5049), 1238–1240, doi:

10.1126/science.255.5049.1238.

Katsura, T., et al. (2009), P-V-T relations of the MgSiO3 perovskite determined by

in situ X-ray diffraction using a large-volume high-pressure apparatus, Geophys.

Res. Lett., 36 (1), L01305, doi:10.1029/2008GL035658.

Kellogg, L. H., and S. D. King (1993), Effect of mantle plumes on the growth of

D′′ by reaction between the core and mantle, Geophys. Res. Lett., 20 (5), 379–382,

doi:10.1029/93GL00045.

Kennett, B. L. N., and E. R. Engdahl (1991), Traveltimes for global earthquake lo-

cation and phase identification, Geophys. J. Int., 105, 429–465, doi:10.1111/j.1365-

246X.1991.tb06724.x.

Keppler, H., L. S. Dubrovinsky, O. Narygina, and I. Kantor (2008), Optical absorption

and radiative thermal conductivity of silicate perovskite to 125 gigapascals, Science,

322, 1529–1532, doi:10.1126/science.1164609.

Kiefer, B., L. Stixrude, and R. M. Wentzcovitch (2002), Elasticity of

142

(Mg,Fe)SiO3–perovskite at high pressures, Geophys. Res. Lett., 29 (11), 1539, doi:

10.1029/2002GL014683.

Kito, T., S. Rost, C. Thomas, and E. J. Garnero (2007), New insights into the P-

and S-wave velocity structure of the D′′ discontinuity beneath the Cocos Plate,

Geophys. J. Int., 169 (2), 631–645, doi:10.1111/j.1365-246X.2007.03350.x.

Knittle, E., and R. Jeanloz (1991), Earth’s core-mantle boundary: Results of exper-

iments at high pressures and temperatures, Science, 251 (5000), 1438–1443, doi:

10.1126/science.251.5000.1438.

Kohler, M. D., J. E. Vidale, and P. M. Davis (1997), Complex scattering within D′′

observed on the very dense Los Angeles Region Seismic Experiment passive array,

Geophys. Res. Lett., 24 (15), 1855–1858, doi:10.1029/97GL01823.

Kono, Y., T. Irifune, Y. Higo, T. Inoue, and A. Barnhoorn (2010), P–V–T relation of

MgO derived by simultaneous elastic wave velocity and in situ x-ray measurements:

A new pressure scale for the mantle transition region, Phys. Earth Planet. In.,

183 (1–2), 196–211, doi:10.1016/j.pepi.2010.03.010.

Lay, T., and D. V. Helmberger (1983), A lower mantle S-wave triplication and the

shear velocity structure of D′′, Geophys. J. Roy. Astr. S., 75 (3), 799–837, doi:

10.1111/j.1365-246X.1983.tb05010.x.

Lay, T., E. J. Garnero, and S. A. Russell (2004), Lateral variation of the D′′

discontinuity beneath the Cocos Plate, Geophys. Res. Lett., 31, L15612, doi:

10.1029/2004GL020300.

143

Lay, T., J. Hernlund, E. J. Garnero, and M. S. Thorne (2006), A post-perovskite

lens and D′′ heat flux beneath the Central Pacific, Science, 314 (5803), 1272–1276,

doi:10.1126/science.1133280.

Lay, T., J. Hernlund, and B. A. Buffett (2008), Core-mantle boundary heat flow, Nat.

Geosci., 1, doi:10.1038/ngeo.2007.44.

Leng, W., and S. Zhong (2008), Viscous heating, adiabatic heating and energetic

consistency in compressible mantle convection, Geophys. J. Int., 173, 693–702, doi:

10.1111/j.1365-246X.2008.03745.x.

Li, B., and J. Zhang (2005), Pressure and temperature dependence of elastic wave

velocity of MgSiO3 perovskite and the composition of the lower mantle, Phys. Earth

Planet. In., 151, 143–154, doi:10.1016/j.pepi.2005.02.004.

Lin, J.-F., and T. Tsuchiya (2008), Spin transition of iron in the Earth’s lower mantle,

Phys. Earth Planet. In., 170, 248–259, doi:10.1016/j.pepi.2008.01.005.

Lin, J.-F., D. L. Heinz, H.-K. Mao, R. J. Hemley, J. M. Devine, J. Li, and G. Shen

(2003), Stability of magnesiowustite in Earth’s lower mantle, P. Natl. Acad. Sci.

USA, 100 (8), 4405–4408, doi:10.1073/pnas.252782399.

Lin, J.-F., S. D. Jacobsen, W. Sturhahn, J. M. Jackson, J. Zhao, and C.-S. Yoo (2006),

Sound velocities of ferropericlase in the Earth’s lower mantle, Geophys. Res. Lett.,

33, L22304, doi:10.1029/2006GL028099.

Lin, J.-F., G. Vanko, S. D. Jacobsen, V. Iota, V. V. Struzhkin, V. B. Prakapenka,

144

A. Kuznetsov, and C.-S. Yoo (2007), Spin transition zone in Earth’s lower mantle,

Science, 317, 1740–1743, doi:10.1126/science.1144997.

Lin, S.-C., and P. E. van Keken (2006), Dynamics of thermochemical plumes: 1.

plume formation and entrainment of a dense layer, Geochem. Geophy. Geosy., 7 (2),

Q02006, doi:10.1029/2005GC001071.

Lithgow-Bertelloni, C., and M. Richards (1998), Dynamics of Cenozoic and Mesozoic

plate motions, Rev. Geophys., 36, 27–78, doi:10.1029/97RG02282.

Liu, L., Y. Tan, D. Sun, M. Chen, and D. Helmberger (2011), Trans-Pacific whole

mantle structure, J. Geophys. Res., 116 (B4), B04306, doi:10.1029/2010JB007907.

Loper, D. E., and I. A. Eltayeb (1986), On the stability of the D′′ layer, Geophys.

Astro. Fluid, 36 (3), 229–255, doi:10.1080/03091928608210086.

Luo, S.-N., S. Ni, and D. V. Helmberger (2001), Evidence for a sharp lateral variation

of velocity at the core-mantle boundary from multipathed PKPab, Earth Planet.

Sc. Lett., 189 (3–4), 155–164, doi:10.1016.S00012-821X(01)00364-8.

Manga, M., and R. Jeanloz (1996), Implications of a metal-bearing chemical boundary

layer in D′′ for mantle dynamics, Geophys. Res. Lett., 23 (22), 3091–3094, doi:

10.1029/96GL03021.

Mao, W. L., G. Shen, V. B. Prakapenka, Y. Meng, A. J. Campbell, D. L. Heinz,

J. Shu, R. J. Hemley, and H.-k. Mao (2004), Ferromagnesian postperovskite silicates

145

in the D′′ layer of the Earth, P. Natl. Acad. Sci. USA, 101 (45), 15,867–15,869, doi:

10.1073/pnas.0407135101.

Mao, W. L., et al. (2005), Iron-rich silicates in the Earth’s D′′ layer, P. Natl. Acad.

Sci. USA, 102 (28), 9751–9753, doi:10.1073/pnas.0503737102.

Mao, W. L., H.-K. Mao, W. Sturhahn, J. Zhao, V. B. Prakapenka, Y. Meng, J. Shu,

Y. Fei, and R. J. Hemley (2006), Iron-rich post-perovskite and the origin of

ultralow-velocity zones, Science, 312, 564–565, doi:10.1126/science.1123442.

Marton, F. C., and R. E. Cohen (2002), Constraints on lower mantle composition

from molecular dynamics simulations of MgSiO3 perovskite, Phys. Earth Planet.

In., 134 (3–4), 239–252, doi:10.1016/S0031-9201(02)00189-9.

Masters, G. (2008), On the possible (1D) seismological signature of the spin crossover

in ferropericlase, Eos Trans. AGU, 89 (53), Fall Meet. Suppl., Abstract MR23A-04.

Masters, G., G. Laske, H. Bolton, and A. Dziewonski (2000), The relative behaviour

of shear velocity, bulk sound speed, and compressional velocity in the mantle:

Implications for chemical and thermal structure, in Earth’s Deep Interior: Mineral

Physics and Tomography From the Atomic to the Global Scale, Geophys. Monogr.

Ser., Vol. 117, edited by S. Karato, A. M. Forte, R. C. Liebermann, G. Masters,

and L. Stixude, pp. 63–87, AGU, Washington, D.C., doi:10.1029/GM117.

Matthews, K. J., A. J. Hale, M. Gurnis, R. D. Muller, and L. DiCaprio (2011),

Dynamic subsidence of Eastern Australia during the Cretaceous, Gondwana Res.,

19, 372–383, doi:10.1016/j.gr.2010.06.006.

146

Matyska, C., and D. A. Yuen (2005), The importance of radiative heat transfer on

superplumes in the lower mantle with the new post-perovskite phase change, Earth

Planet. Sc. Lett., 234, 71–81, doi:10.1016/j.epsl.2004.10.040.

Matyska, C., and D. A. Yuen (2006), Lower mantle dynamics with the post-perovskite

phase change, radiative thermal conductivity, temperature- and depth-dependent

viscosity, Phys. Earth Planet. In., 154, 196–207, doi:10.1016/j.pepi.2005.10.001.

McNamara, A. K., and S. Zhong (2004), Thermochemical structures within a

spherical mantle: Superplumes or piles?, J. Geophys. Res., 109, B07402, doi:

10.1029/2003JB002847.

McNamara, A. K., and S. Zhong (2005), Thermochemical structures beneath Africa

and the Pacific Ocean, Nature, 437, doi:10.1038/nature04066.

McNamara, A. K., E. J. Garnero, and S. Rost (2010), Tracking deep mantle reser-

voirs with ultra-low velocity zones, Earth Planet. Sc. Lett., 299 (1–2), 1–9, doi:

10.1016/j.epsl.2010.07.042.

Monnereau, M., and D. A. Yuen (2007), Topology of the postperovskite phase tran-

sition and mantle dynamics, P. Natl. Acad. Sci. USA, 104 (22), 9156–9161, doi:

10.1073/pnas.0608480104.

Moresi, L., and V. Solomatov (1998), Mantle convection with a brittle lithosphere:

thoughts on the global tectonic styles of the Earth and Venus, Geophys. J. Int.,

133, 669–682, doi:10.1046/j.1365-246X.1998.00521.x.

147

Mori, J., and D. V. Helmberger (1995), Localized boundary layer below the Mid-

Pacific velocity anomaly identified from a PcP precursor, J. Geophys. Res.,

100 (B10), 20,359–20,365, doi:10.1029/95JB02243.

Mosenfelder, J. L., P. D. Asimow, D. J. Frost, D. C. Rubie, and T. J. Ahrens (2009),

The MgSiO3 system at high pressure: Thermodynamic properties of perovskite,

postperovskite, and melt from global inversion of shock and static compression

data, J. Geophys. Res., 114, B01203, doi:10.1029/2008JB005900.

Murakami, M., K. Hirose, K. Kawamura, N. Sata, and Y. Ohishi (2004),

Post-perovskite phase transition in MgSiO3, Science, 304 (5672), 855–858, doi:

10.1126/science.1095932.

Murakami, M., K. Hirose, N. Sata, and Y. Ohishi (2005), Post-perovskite phase

transition and mineral chemistry in the pyrolitic lowermost mantle, Geophys. Res.

Lett., 32, L03304, doi:10.1029/2004GL021956.

Murakami, M., S. V. Sinogeikin, J. D. Bass, N. Sata, Y. Ohishi, and K. Hirose

(2007), Sound velocity of MgSiO3 post-perovskite phase: a constraint on the D′′

discontinuity, Earth Planet. Sc. Lett., 259, 18–23, doi:10.1016/j.epsl.2007.04.015.

Nakagawa, T., and P. J. Tackley (2004), Effects of a perovskite-post perovskite phase

change near core-mantle boundary in compressible mantle convection, Geophys.

Res. Lett., 31, L16611, doi:10.1029/2004gl020648.

Naliboff, J. B., and L. H. Kellogg (2006), Dynamic effects of a step-wise increase in

148

thermal conductivity and viscosity in the lowermost mantle, Geophys. Res. Lett.,

33, L12S09, doi:10.1029/2006GL025717.

Ni, S., and D. V. Helmberger (2001a), Probing an ultra-low velocity zone at the core

mantle boundary with P and S waves, Geophys. Res. Lett., 28 (12), 2345–2348,

doi:10.1029/2000GL012766.

Ni, S., and D. V. Helmberger (2001b), Horizontal transition from fast to slow struc-

tures at the core-mantle boundary; South Atlantic, Earth Planet. Sc. Lett., 187 (3–

4), 301–310, doi:10.1016/S0012-821X(01)00273-4.

Ni, S., and D. V. Helmberger (2003a), Seismological constraints on the South African

superplume; could be the oldest distinct structure on Earth, Earth Planet. Sc. Lett.,

206, 119–131, doi:10.1016/S0012-821X(02)01072-5.

Ni, S., and D. V. Helmberger (2003b), Ridge-like lower mantle structure beneath

South Africa, J. Geophys. Res., 108 (B2), 2094, doi:10.1029/2001JB001545.

Ni, S., and D. V. Helmberger (2003c), Further constraints on the African superplume

structure, Phys. Earth Planet. In., 140, 243–251, doi:10.1016/j.pepi.2003.07.011.

Ni, S., X. Ding, D. V. Helmberger, and M. Gurnis (1999), Low-velocity structure

beneath Africa from forward modeling, Earth Planet. Sc. Lett., 170 (4), 497–507,

doi:10.1016/S0012-821X(99)00121-1.

Ni, S., X. Ding, and D. V. Helmberger (2000), Constructing synthetics from deep

149

Earth tomographic models, Geophys. J. Int., 140, 71–82, doi:10.1046/j.1365-

246x.2000.00982.x.

Ni, S., E. Tan, M. Gurnis, and D. V. Helmberger (2002), Sharp sides to the African

superplume, Science, 296, 1850–1852, doi:10.1126/science.1070698.

Ni, S., D. V. Helmberger, and J. Tromp (2005), Three-dimensional structure of the

African superplume from waveform modelling, Geophys. J. Int., 161, 283–294, doi:

10.1111/j.1365-246X.2005.02508.x.

Niu, F., and L. Wen (2001), Strong seismic scatterers near the core-mantle

boundary west of Mexico, Geophys. Res. Lett., 28 (18), 3557–3560, doi:

10.1029/2001GL013270.

Oganov, A. R., and S. Ono (2004), Theoretical and experimental evidence for a

post-perovskite phase of MgSiO3 in Earth’s D′′ layer, Nature, 430, 445–448, doi:

10.1038/nature02701.

Oganov, A. R., J. P. Brodholt, and G. D. Price (2001), The elastic constants of

MgSiO3 perovskite at pressures and temperatures of the Earth’s mantle, Nature,

411, 934–937, doi:10.1038/35082048.

Olson, P., and D. A. Yuen (1982), Thermochemical plumes and mantle phase transi-

tions, J. Geophys. Res., 87 (B5), 3993–4002, doi:10.1029/JB087iB05p03993.

Olson, P., G. Schubert, and C. Anderson (1987), Plume formation in the D′′-layer

and the roughness of the core-mantle boundary, Nature, 327, 409–413.

150

O’Neill, C., R. D. Muller, and B. Steinberger (2005), On the uncertainties in hot spot

reconstructions and the significance of moving hot spot reference frames, Geochem.

Geophy. Geosy., 6, Q04003, doi:10.1029/2004GC000784.

Reasoner, C., and J. Revenaugh (2000), ScP constraints on ultralow-velocity zone

density and gradient thickness beneath the Pacific, J. Geophys. Res., 105 (B12),

28,173–28,182, doi:10.1029/2000JB900331.

Ren, Y., E. Stutzmann, R. D. van der Hilst, and J. Besse (2007), Understand-

ing seismic heterogeneities in the lower mantle beneath the Americas from seis-

mic tomography and plate tectonic history, J. Geophys. Res., 112, B01302, doi:

10.1029/2005JB004154.

Revenaugh, J., and R. Meyer (1997), Seismic evidence of partial melt within a possibly

ubiquitous low-velocity layer at the base of the mantle, Science, 277 (5326), 670–

673, doi:10.1126/science.277.5326.670.

Richards, M. A., and D. C. Engebretson (1992), Large-scale mantle convection and

the history of subduction, Nature, 355, 437–440, doi:10.1038/355437a0.

Richter, F. (1973), Finite amplitude convection through a phase boundary, Geophys.

J. Roy. Astr. S., 35, 265–276, doi:10.1111/j.1365-246X.1973.tb02427.x.

Richter, F. M., and D. P. McKenzie (1981), On some consequences and possible

causes of layered mantle convection, J. Geophys. Res., 86 (B7), 6133–6142, doi:

10.1029/JB086iB07p06133.

151

Ringwood, A. E. (1991), Phase transformations and their bearing on the constitution

and dynamics of the mantle, Geochim. Cosmochim. Ac., 55 (8), 2083–2110, doi:

10.1016/0016-7037(91)90090-R.

Ritsema, J., S. Ni, D. V. Helmberger, and H. P. Crotwell (1998), Evidence for strong

shear velocity reductions and velocity gradients in the lower mantle beneath Africa,

Geophys. Res. Lett., 25 (23), 4245–4248, doi:10.1029/1998GL900127.

Ritsema, J., H. J. van Heijst, and J. H. Woodhouse (1999), Complex shear wave

velocity structure imaged beneath Africa and Iceland, Science, 286, 1925–1928,

doi:10.1126/science.286.5446.1925.

Ritsema, J., A. Deuss, H. J. van Heijst, and J. H. Woodhouse (2011), S40RTS: a

degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion,

teleseismic traveltime and normal-mode splitting function measurements, Geophys.

J. Int., 184 (3), 1223–1236, doi:10.1111/j.1365-246X.2010.04884.x.

Rondenay, S., and K. M. Fischer (2003), Constraints on localized core-mantle bound-

ary structure from multichannel, broadband SKS coda analysis, J. Geophys. Res.,

108 (B11), 2537, doi:10.1029/2003JB002518.

Rost, S., and J. Revenaugh (2003), Small-scale ultralow-velocity zone structure im-

aged by ScP, J. Geophys. Res., 108 (B1), 2056, doi:10.1029/2001JB001627.

Rost, S., E. J. Garnero, Q. Williams, and M. Manga (2005), Seismological constraints

on a possible plume root at the core-mantle boundary, Nature, 435, 666–669, doi:

10.1038/nature03620.

152

Rost, S., E. J. Garnero, and Q. Williams (2006), Fine-scale ultralow-velocity zone

structure from high-frequency seismic array data, J. Geophys. Res., 111, doi:

10.1029/2005JB004088.

Rost, S., E. J. Garnero, M. S. Thorne, and A. R. Hutko (2010a), On the absence

of an ultralow-velocity zone in the North Pacific, J. Geophys. Res., 115, B04312,

doi:10.1029/2009JB006420.

Rost, S., E. J. Garnero, and W. Stefan (2010b), Thin and intermittent ultralow-

velocity zones, J. Geophys. Res., 115, B06312, doi:10.1029/2009JB006981.

Sakai, T., et al. (2009), Fe–Mg partitioning between perovskite and ferropericlase in

the lower mantle, Am. Mineral., 94, 921–925, doi:10.2138/am.2009.3123.

Schubert, G., D. A. Yuen, and D. L. Turcotte (1975), Role of phase transitions in

a dynamic mantle, Geophys. J. Roy. Astr. S., 42, 705–735, doi:10.1111/j.1365-

246X.1975.tb05888.x.

Seagle, C. T., D. L. Heinz, A. J. Campbell, V. B. Prakapenka, and S. T. Wanless

(2008), Melting and thermal expansion in the Fe-FeO system at high pressure,

Earth Planet. Sc. Lett., 265 (3–4), 655–665, doi:10.1016/j.epsl.2007.11.004.

Seton, M., et al. (2012), Global continental and ocean basin reconstructions since 200

Ma, Earth-Sc. Rev., doi:10.1016/j.earscirev.2012.03.002, (in press).

Shim, S.-H. (2008), The postperovskite transition, Ann. Rev. Earth Pl. Sc., 36, 569–

599, doi:10.1146/annurev.earth.36.031207.124309.

153

Sidorin, I., and M. Gurnis (1998), Geodynamically consistent seismic velocity pre-

dictions at the base of the mantle, in The Core-Mantle Boundary Region, Geodyn.

Ser., Vol. 28, edited by M. Gurnis, M. Wysession, E. Knittle, and B. A. Buffett,

pp. 209–230, AGU, Washington, D.C.

Sidorin, I., M. Gurnis, D. V. Helmberger, and X. Ding (1998), Interpreting D′′ seismic

structure using synthetic waveforms computed from dynamic models, Earth Planet.

Sc. Lett., 163, 31–41, doi:10.1016/S0012-821X(98)00172-1.

Sidorin, I., M. Gurnis, and D. V. Helmberger (1999a), Dynamics of a phase change

at the base of the mantle consistent with seismological observations, J. Geophys.

Res., 104 (B7), 15,005–15,023, doi:10.1029/1999JB900065.

Sidorin, I., M. Gurnis, and D. V. Helmberger (1999b), Evidence for a ubiquitous

seismic discontinuity at the base of the mantle, Science, 286, 1326–1331, doi:

10.1126/science.286.5443.1326.

Simmons, N. A., and S. P. Grand (2002), Partial melting in the deepest mantle,

Geophys. Res. Lett., 29 (11), 1552, doi:10.1029/2001GL013716.

Sinmyo, R., K. Hirose, D. Nishio-Hamane, Y. Seto, K. Fujino, N. Sata, and Y. Ohishi

(2008), Partitioning of iron between perovskite/postperovskite and ferropericlase

in the lower mantle, J. Geophys. Res., 113, B11204, doi:10.1029/2008JB005730.

Sleep, N. H. (1988), Gradual entrainment of a chemical layer at the base of the

mantle by overlying convection, Geophys. J. Int., 95, 437–447, doi:10.1111/j.1365-

246X.1988.tb06695.x.

154

Solheim, L. P., and W. R. Peltier (1990), Heat transfer and the onset of chaos in

a spherical, axisymmetric, anelastic models of whole mantle convection, Geophys.

Astro. Fluid, 53 (4), 205–255.

Stacey, F. D. (1977), A thermal model of the Earth, Phys. Earth Planet. In., 15 (4),

341–348, doi:10.1016/0031-9201(77)90096-6.

Stackhouse, S., and J. P. Brodholt (2008), Elastic properties of the post-perovskite

phase of Fe2O3 and implications for ultra-low velocity zones, Phys. Earth Planet.

In., 170, 260–266, doi:10.1016/j.pepi.2008.07.010.

Stackhouse, S., J. P. Brodholt, J. Wookey, J.-M. Kendall, and G. D. Price (2005),

The effect of temperature on the seismic anisotropy of the perovskite and post-

perovskite polymorphs of MgSiO3, Earth Planet. Sc. Lett., 230 (1–2), 1–10, doi:

10.1016/j.epsl.2004.11.021.

Stadler, G., M. Gurnis, C. Burstedde, L. C. Wilcox, L. Alisic, and O. Ghattas (2010),

The dynamics of plate tectonics and mantle flow: from local to global scales, Sci-

ence, 329, 1033–1038, doi:10.1126/science.1191223.

Stampfli, G., and G. Borel (2002), A plate tectonic model for the Paleozoic

and Mesozoic constrained by dynamic plate boundaries and restored synthetic

oceanic isochrons, Earth Planet. Sc. Lett., 196 (1–2), 17–33, doi:10.1016/S0012-

821X(01)00588-X.

Steinbach, V., and D. A. Yuen (1994), Effects of depth-dependent properties on the

155

thermal anomalies produced in flush instabilities from phase transitions, Phys.

Earth Planet. In., 86 (1–3), 165–183, doi:10.1016/0031-9201(94)05067-8.

Steinbach, V., U. Hansen, and A. Ebel (1989), Compressible convection in the Earth’s

mantle: a comparison of different approaches, Geophys. Res. Lett., 16 (7), 633–636.

Steinberger, B., and T. H. Torsvik (2008), Absolute plate motions and true po-

lar wander in the absence of hotspot tracks, Nature, 452 (7187), 620–623, doi:

10.1038/nature06824.

Steinberger, B., and T. H. Torsvik (2010), Toward an explanation for the present

and past locations of the poles, Geochem. Geophy. Geosy., 11 (6), Q06W06, doi:

10.1029/2009GC002889.

Steinberger, B., and T. H. Torsvik (2011), A geodynamic model of plumes from the

margins of Large Low Shear Velocity Provinces, Geochem. Geophy. Geosy., 13 (1),

Q01W09, doi:10.1029/2011GC003808.

Sturhahn, W., J. M. Jackson, and J.-F. Lin (2005), The spin state of iron in minerals of

Earth’s lower mantle, Geophys. Res. Lett., 32, L12307, doi:10.1029/2005GL022802.

Su, W.-J., and A. M. Dziewonski (1997), Simultaneous inversion for 3-D variations in

shear and bulk velocity in the mantle, Phys. Earth Planet. In., 100 (1–4), 35–156,

doi:10.1016/S0031-9201(96)03236-0.

Sun, D., and D. Helmberger (2008), Lower mantle tomography and phase change

mapping, J. Geophys. Res., 113, B10305, doi:10.1029/2007JB005289.

156

Sun, D., T.-R. A. Song, and D. Helmberger (2006), Complexity of D′′ in the pres-

ence of slab-debris and phase changes, Geophys. Res. Lett., 33, L12S07, doi:

10.1029/2005GL025384.

Sun, D., E. Tan, D. Helmberger, and M. Gurnis (2007), Seismological sup-

port for the metastable superplume model, sharp features, and phase changes

within the lower mantle, P. Natl. Acad. Sci. USA, 104 (22), 9151–9155, doi:

10.1073/pnas.0608160104.

Sun, D., D. Helmberger, and M. Gurnis (2009a), Chemical piles and deep mantle

plumes, in preparation.

Sun, D., D. Helmberger, S. Ni, and D. Bower (2009b), Direct measures of lat-

eral velocity variation in the deep Earth, J. Geophys. Res., 114, B05303, doi:

10.1029/2008JB005873.

Sun, D., D. Helmberger, and M. Gurnis (2010), A narrow, mid-mantle plume below

southern Africa, Geophys. Res. Lett., 37 (9), L09302, doi:10.1029/2009GL042339.

Tackley, P. (2000), Self-consistent generation of tectonic plates in time-dependent,

three-dimensional mantle convection simulations 1. pseudoplastic yielding,

Geochem. Geophy. Geosy., 1 (1), 1021, doi:10.1029/2000GC000036.

Tackley, P. J. (1998), Three-dimensional simulations of mantle convection with a

thermo-chemical basal boundary layer: D′′?, in The Core-Mantle Boundary Region,

Geodyn. Ser., Vol. 28, edited by M. Gurnis, M. Wysession, E. Knittle, and B. A.

Buffett, pp. 231–254, AGU, Washington, D.C., doi:10.1029/GD028.

157

Tackley, P. J. (2002), Strong heterogeneity caused by deep mantle layering, Geochem.

Geophy. Geosy., 3 (4), doi:10.1029/2001GC000167.

Tackley, P. J. (2011), Living dead slabs in 3-D: The dynamics of compositionally-

stratified slabs entering a “slab-graveyard” above the core-mantle boundary, Phys.

Earth Planet. In., 188 (3–4), 150–162, doi:10.1016/j.pepi.2011.04.013.

Tackley, P. J., and S. King (2003), Testing the tracer ratio method for modeling active

compositional fields in mantle convection simulations, Geochem. Geophy. Geosy.,

4 (4), 8302, doi:10.1029/2001GC000214.

Takeuchi, N., Y. Morita, N. D. Xuyen, and N. Q. Zung (2008), Extent of the low-

velocity region in the lowermost mantle beneath the western Pacific detected by

the Vietnamese broadband seismograph array, Geophys. Res. Lett., 35 (5), L05307,

doi:10.1029/2008GL033197.

Tan, E., and M. Gurnis (2005), Metastable superplumes and mantle compressibility,

Geophys. Res. Lett., 32, L20307, doi:10.1029/2005GL024190.

Tan, E., and M. Gurnis (2007), Compressible thermochemical convection and

application to lower mantle structures, J. Geophys. Res., 112, B06304, doi:

10.1029/2006JB004505.

Tan, E., M. Gurnis, and L. Han (2002), Slabs in the lower mantle and their

modulation of plume formation, Geochem. Geophy. Geosy., 3 (11), 1067, doi:

10.1029/2001GC000238.

158

Tan, E., W. Leng, S. Zhong, and M. Gurnis (2007), Citcoms v3.0 - a compressible

thermo-chemical mantle convection code, Eos Trans. AGU, 88 (52), Fall Meet.

Suppl., Abstract DI14A-01.

Tan, E., W. Leng, S. Zhong, and M. Gurnis (2011), On the location of plumes

and lateral movement of thermo-chemical structures with high bulk modulus in

the 3-D compressible mantle, Geochem. Geophy. Geosy., 12 (7), Q07005, doi:

10.1029/2011GC003665.

Tateno, S., K. Hirose, N. Sata, and Y. Ohishi (2007), Solubility of FeO in (Mg,Fe)SiO3

perovskite and the post-perovskite phase transition, Phys. Earth Planet. In., 160 (3-

4), 319–325, doi:10.1016/j.pepi.2006.11.010.

Thomas, C., E. J. Garnero, and T. Lay (2004), High-resolution imaging of lower-

most mantle structure under the Cocos Plate, J. Geophys. Res., 109, B08307, doi:

10.1029/2004JB003013.

Thompson, P. F., and P. J. Tackley (1998), Generation of mega-plumes from the core-

mantle boundary in a compressible mantle with temperature-dependent viscosity,

Geophys. Res. Lett., 25 (11), 1999–2002, doi:10.1029/98GL01228.

Thorne, M. S., and E. J. Garnero (2004), Inferences on ultralow-velocity zone struc-

ture from a global analysis of SPdKS waves, J. Geophys. Res., 109, B08301, doi:

10.1029/2004JB003010.

To, A., B. A. Romanowicz, Y. Capdeville, and N. Takeuchi (2005), 3D effects of sharp

159

boundaries at the borders of the African and Pacific Superplumes: Observation and

modeling, Earth Planet. Sc. Lett., 233, 137–153, doi:10.1016/j.epsl.2005.01.037.

Torsvik, T. H., K. Burke, B. Steinberger, S. J. Webb, and L. D. Ashwal (2010),

Diamonds sampled by plumes from the core-mantle boundary, Nature, 466, doi:

10.1038/nature09216.

Tsuchiya, T., J. Tsuchiya, K. Umemoto, and R. M. Wentzcovitch (2004), Elas-

ticity of post-perovskite MgSiO3, Geophys. Res. Lett., 31 (14), L14603, doi:

10.1029/2004GL020278.

Tsuchiya, T., R. M. Wentzcovitch, C. R. da Silva, and S. de Gironcoli (2006), Spin

transition in magnesiowustite in Earth’s lower mantle, Phys. Rev. Lett., 96, 198501,

doi:10.1103/PhysRevLett.96.198501.

van der Meer, D. G., W. Spakman, D. J. J. van Hinsbergen, M. L. Amaru, and T. H.

Torsvik (2010), Towards absolute plate motions constrained by lower-mantle slab

remnants, Nat. Geosci., 3, 36–40, doi:10.1038/ngeo708.

Vidale, J. E., and M. A. H. Hedlin (1998), Evidence for partial melt at the core-mantle

boundary north of Tonga from the strong scattering of seismic waves, Nature, 391,

682–685, doi:10.1038/35601.

Vincent, A. P., and D. A. Yuen (1988), Thermal attractor in chaotic convec-

tion with high-Prandtl-number fluids, Physical Review A, 38 (1), 328–334, doi:

10.1103/PhysRevA.38.328.

160

Wang, Y., and L. Wen (2004), Mapping the geometry and geographic distribution of

a very low velocity province at the base of the Earths mantle, J. Geophys. Res.,

109, B10305, doi:10.1029/2003JB002674.

Wang, Y., and L. Wen (2007a), Geometry and P and S velocity structure of the

“African Anomaly”, J. Geophys. Res., 112, B05313, doi:10.1029/2006JB004483.

Wang, Y., and L. Wen (2007b), Complex seismic anisotropy at the border of a very

low velocity province at the base of the Earths mantle, J. Geophys. Res., 112,

B09305, doi:10.1029/2006JB004719.

Watt, J. P., G. F. Davies, and R. J. O’Connell (1976), The elastic properties of com-

posite materials, Rev. Geophys., 14 (4), 541–563, doi:10.1029/RG014I004P00541.

Wen, L. (2000), Intense seismic scattering near the Earth’s core-mantle bound-

ary beneath the Comoros hotspot, Geophys. Res. Lett., 27 (22), 3627–3630, doi:

10.1029/2000GL011831.

Wen, L. (2001), Seismic evidence for a rapidly varying compositional anomaly at

the base of the Earth’s mantle beneath the Indian Ocean, Earth Planet. Sc. Lett.,

194 (1–2), 83–95, doi:10.1016/S0012-821X(01)00550-7.

Wen, L. (2002), An SH hybrid method and shear velocity structures in the lowermost

mantle beneath the Central Pacific and South Atlantic Oceans, J. Geophys. Res.,

107 (B3), doi:10.1029/2001JB000499.

Wen, L. (2006), A compositional anomaly at the Earth’s core-mantle boundary as an

161

anchor to the relatively slowly moving surface hotspots and as as source to the DU-

PAL anomaly, Earth Planet. Sc. Lett., 246, 138–148, doi:10.1016/j.epsl.2006.04.024.

Wen, L., and D. V. Helmberger (1998a), A two-dimensional P–SV hybrid method and

its application to modeling localized structures near the core-mantle boundary, J.

Geophys. Res., 103 (B8), 17,901–17,918, doi:10.1029/98JB01276.

Wen, L., and D. V. Helmberger (1998b), Ultra-low velocity zones near the core-

mantle boundary from broadband PKP precursors, Science, 279, 1701–1703, doi:

10.1126/science.279.5357.1701.

Wen, L., P. Silver, D. James, and R. Kuehnel (2001), Seismic evidence for a thermo-

chemical boundary at the base of the Earth’s mantle, Earth Planet. Sc. Lett., 189,

141–153, doi:10.1016/S0012-821X(01)00365-X.

Wentzcovitch, R. M., T. Tsuchiya, and J. Tsuchiya (2006), MgSiO3 post-

perovskite at D′′ conditions, P. Natl. Acad. Sci. USA, 103, 543–546, doi:

10.1073/pnas.0506879103.

Wessel, P., and L. W. Kroenke (2008), Pacific absolute plate motion since 145 Ma: An

assessment of the fixed hot spot hypothesis, J. Geophys. Res., 113 (B6), B06101,

doi:10.1029/2007JB005499.

Wessel, P., Y. Harada, and L. W. Kroenke (2006), Toward a self-consistent, high-

resolution absolute plate motion model for the Pacific, Geochem. Geophy. Geosy.,

7 (3), Q03L12, doi:10.1029/2005GC001000.

162

Wicks, J. K., J. M. Jackson, and W. Sturhahn (2010), Very low sound velocities in

iron-rich (Mg,Fe)O: Implications for the core-mantle boundary region, Geophys.

Res. Lett., 37, L15304, doi:10.1029/2010GL043689.

Williams, Q., and E. J. Garnero (1996), Seismic evidence for partial melt at the base

of Earth’s mantle, Science, 273, 1528–1530, doi:10.1126/science.273.5281.1528.

Williams, Q., J. Revenaugh, and E. Garnero (1998), A correlation between ultra-

low basal velocities in the mantle and hot spots, Science, 281, 546–549, doi:

10.1126/science.281.5376.546.

Wookey, J., S. Stackhouse, J.-M. Kendall, J. Brodholt, and G. D. Price (2005), Effi-

cacy of the post-perovskite phase as an explanation for lowermost-mantle seismic

properties, Nature, 438, doi:10.1038/nature04345.

Wysession, M. E., T. Lay, J. Revenaugh, Q. Williams, E. Garnero, R. Jeanloz, and

L. H. Kellogg (1998), The D′′ discontinuity and its implications, in The Core-

Mantle Boundary Region, Geodyn. Ser., Vol. 28, edited by M. Gurnis, M. Wyses-

sion, E. Knittle, and B. A. Buffett, pp. 273–297, AGU, Washington, D.C., doi:

10.1029/GD028.

Yamazaki, D., and S. Karato (2001), Some mineral physics constraints on the rheology

and geothermal structure of Earth’s lower mantle, Am. Mineral., 86 (4), 385–391.

Young, C. J., and T. Lay (1987), Evidence for a shear velocity discontinuity in the

lower mantle beneath India and the Indian Ocean, Phys. Earth Planet. In., 49 (1–2),

37–53, doi:10.1016/0031-9201(87)90131-2.

163

Young, C. J., and T. Lay (1990), Multiple phase analysis of the shear velocity struc-

ture in the D′′ region beneath Alaska, J. Geophys. Res., 95 (B11), 17,385–17,402,

doi:10.1029/JB095iB11p17385.

Youngs, B. A. R., and G. A. Houseman (2009), Formation of steep-sided topography

from compositionally distinct dense material at the base of the mantle, J. Geophys.

Res., 114, B04404, doi:10.1029/2007JB005487.

Yuen, D. A., and W. R. Peltier (1980), Mantle plumes and the thermal stability of

the D′′ layer, Geophys. Res. Lett., 7 (9), 625–628, doi:10.1029/GL007I009P00625.

Zhang, N., S. Zhong, W. Leng, and Z.-X. Li (2010), A model for the evolution of the

Earth’s mantle structure since the early Paleozoic, J. Geophys. Res., 115, B06401,

doi:10.1029/2009JB006896.

Zhang, Y., J. Ritsema, and M. Thorne (2009), Modeling the ratios of SKKS and SKS

amplitudes with ultra-low velocity zones at the core-mantle boundary, Geophys.

Res. Lett., 36, L19303, doi:10.1029/2009GL040030.

Zhao, W., and D. A. Yuen (1987), The effects of adiabatic and viscous heatings on

plumes, Geophys. Res. Lett., 14 (12), 1223–1226, doi:10.1029/GL014i012p01223.

Zhong, S., M. Zuber, L. N. Moresi, and M. Gurnis (2000), Role of temperature-

dependent viscosity and surface plates in spherical shell models of mantle convec-

tion, J. Geophys. Res., 105 (B5), 11,063–11,082, doi:10.1029/2000JB900003.

Zhong, S., N. Zhang, Z.-X. Li, and J. H. Roberts (2007), Supercontinent cycles, true

164

polar wander, and very long-wavelength mantle convection, Earth Planet. Sc. Lett.,

261, 551–564, doi:10.1016/j.epsl.2007.07.049.

Zhong, S., A. McNamara, E. Tan, L. Moresi, and M. Gurnis (2008), A benchmark

study on mantle convection in a 3-D spherical shell using CitcomS, Geochem. Geo-

phy. Geosy., 9 (10), Q10017, doi:10.1029/2008GC002048.